During the second world war, Michel Houellebecq's father witnessed two French resistance fighters killing a Nazi officer in the Paris metro. "He concluded that it was 'not very interesting,'" writes Houellebecq. "I can still picture him as he said those words and I did not question him further."

When Bernard-Henri Lévy's replies to Houellebecq's letter in which this account appears, you can almost hear the steam coming out of his ears. "What I find worrying is how you use the anecdote and your way of being apparently satisfied with the most pessimistic, the most distressing explanation, as if this indifference suited you today." Lévy charges Houellebecq, by not taking sides, of putting the absolute evil of Nazism on a moral level with resistance to it. This exchange goes to the heart of the conflict between two French writers who for five months in 2008 took part in a snarling correspondence that, belatedly, is now published here. "We have, as they say, nothing in common," writes Houellebecq mordantly at the outset, "except we are both rather contemptible individuals." He casts Lévy as a philosopher without original ideas specialising in farcical media stunts, and himself as a nihilist, as reactionary, cynical, racist and a shameless misogynist.

Of course, neither France's most celebrated living novelist nor its most famous living philosopher believes such media-imposed descriptions of themselves. At worst, Public Enemies is as edifying as reading Hugh Grant and Steve Coogan lick each other's journalist-inflicted wounds. Fortunately, the book doesn't stay in media whine mode for long but reverts to a clash between an engagé Sartrean intellectual par excellence and the politically disengaged, sometimes self-pitying Houellebecq.

"[A]ll I can do is shut up and accept that I live in a world where the general will exercises too great a pressure on the will of the individual," writes Houellebecq. "In practice I can try to find a corner where I can go and die, some isolated spot where, all alone, I can give myself over to my modest vices." Not an appealing way to write about Ireland, where Houellebecq has secreted himself, but he thereby becomes spiritual sibling to Lynne Truss, author of Talk to the Hand: Six Good Reasons to Stay Home and Bolt the Door.

Who is the bigger espèce de connard? I'm torn. When I interviewed BHL for a TV programme on French philosophy in his Boulevard Saint Germain apartment, he leaned forward to make a point in a shirt open to the tummy, revealing his nipples for BBC4. But now, confronted with Houellebecq's sub-Generation X ennui, I can't help but applaud the preening, self-righteous narcissist.

And yet, when Houellebecq writes of his political disengagement, he has a grip on a cynical west European temper antipathetic to Lévy, and anatomises it mercilessly. He claims never to have had the sense of inhabiting a democracy. Rather, he has always lived supinely in technocracies, "though without necessarily feeling that was a bad thing".

He says he regards public space as "a hostile territory bristling with absurd and humiliating bans"  he is, naturellement, a smoker  "which I negotiate as quickly as possible to get from one private residence to another private residence." His antisocial politics may be insufferable to Lévy, but they're widely shared.

Lévy is no match for Houellebecq's caustic wit, which will be familiar from his novels. Houellebecq suggests that French economic recovery must be predicated on serving Asian tourists cheese, Romanesque churches and confit de canard. "Does anyone really believe we're going to become world leaders in software development or microprocessors?  To put it more crudely, do I really want to turn France into a dead, mummified country, a sort of tourist brothel?  Without a second thought, I say YES."

Lévy is better read but less fun, riffing earnestly about Lucretius's atomic theory, Leibniz's monadology, Levinas's conceptualisation of the Other. Houellebecq writes back wearily that he hasn't read those books and yearns to return to Russia with its joie de vivre and nightclubs filled with "sumptuous blondes". He's surely winding up his correspondent. If so, it works, for Lévy rages back: "This Russia  believes in nothing at all, absolutely nothing, just the religion of the marketplace, consumption and brands." It's a shame this remark is published in a month engagé Russians are demonstrating against Putin.

After circling each other, both dive into the confessional mode they affect to disdain. Each confesses to type: Michel prefers to make love while semi-conscious, Bernard-Henri while on high alert (one imagines him staring, existentially, into the very soul of his lover during sex, which must be rather trying).

We're nobodies in our homeland, Houellebecq argues at one point: "We're not even mentioned in the credits of Ratatouille." Another imposture: in agreeing to the publication of this book (and seeing it become a number one bestseller in France), each has a well-developed sense of his own and his correspondent's significance. And, while enjoying the exchange, we needn't share its self-importance: this isn't a clash of the titans, hardly Rousseau v Hume.

But it does raise the question: which two intellos d'outre Manche could perform a similarly diverting epistolary dance? Niall Ferguson v Eric Hobsbawm? Dawkins v Scruton? Greer v Starkey? Perhaps we must accept that the French are not just better at wine, cheese, sex, style, football, film and sucking up to Angela Merkel, but also at eviscerating each other in books. Chapeau, messieurs!

In 2008, after what you imagine was a tired and emotional dinner, the novelist Michel Houellebecq and the philosopher Bernard-Henri Lévy determined to start writing to each other about the things that kept them awake at nights. For six months, they corresponded on subjects that ranged from eczema to Epicurus, from Sarkozy to Sartre. Mostly, though, in the course of this strangely compulsive, wildly self-absorbed exchange, which ultimately ran to these 300 pages, they dwelt on the trait that seemed to have most united them in the public mind: "We are," as Houellebecq acknowledges in his opening letter, "both rather contemptible individuals."

This fact leads to the fundamental question of their engagement. Why are they so hated? Houellebecq begins by counting the ways. Lévy, he attests, is a "philosopher without an original idea but with excellent contacts", a "specialist in farcical media stunts", the "obscenely wealthy epitome of champagne socialism", the creator of the "most preposterous film in history" (the fabulously bad Le jour et la nuit), a man who even gives his trademark white shirts, provocatively unbuttoned to near the waist, a bad name.

The novelist, most famous for the bleak sexual odyssey of his worldwide bestseller Atomised, published a decade ago, is no less blunt about his own failings: "Nihilist, reactionary, cynic, racist, shameless misogynist," he suggests, "an unremarkable author with no style"; a redneck depressionist who "achieved literary notoriety some years ago as the result of an uncharacteristic error in judgment by critics who had lost the plot".

What follows is a discursive and often scabrously comic (deliberately and not) meditation on what Lévy identifies as the secret desire of all writers  "the desire to displease, to be repudiated. The giddiness and pleasure of disgrace". There is no limit to the self-flagellation, the googled humiliations, the slights and slanders sharply remembered across decades that follow. Lévy at one point dwells, for example, on the Parisian trend for "idiot dinners", which apparently are fashionable among the city's intelligentsia each time his dire film is repeated on French TV, where "the idiots are the film and its author".

As the correspondence unfolds, each man begins to identify both the sources of the rancour he excites and the defence against it. For Lévy, sanity always lies in narcissism: "In the face of assaults my ego is fireproof, shatterproof." Houellebecq, meanwhile, claims at times to draw strength from the outrage he provokes, though generally he believes that "what I am going through is something similar to what medieval criminals did when they were pilloried head imprisoned in a wooden frame and any passer-by could slap him in the face, spit at him or worse".

There is, of course, a good deal that is self-serving about both of these perceived predicaments (as they both well know). Martyrdom is among the least honest and most seductive of human states. If they are united in their sense of being contemptible, they have, moreover, an implacable solidarity against the sources of all that contempt. As writers, they see their bodies of work as host to a small army of parasitical critics, evolved to irritate and destroy, and try as they might they cannot stop itching. The life of the mind is plagued by the indefatigable corporeal tormentors of the books pages. Individuals from Le Figaro and Le Monde are singled out for special retaliatory delousing.

In some senses, Houellebecq, the Nietzschean, expects nothing less of his public; he takes pride in his pariah status (he is a self-styled exile, having moved to Connemara to escape the savagery of his compatriots, in particular those who pushed for his prosecution after he noted that "Islam was the stupidest of all religions"). Lévy, for his part, takes pride pretty much anywhere he can find it. They compete for kinship with the great misunderstood outsiders of the past: Rimbaud and Baudelaire, Dostoevsky and Voltaire.

Though they begin by taking as read their political differences  Lévy a man of the "moral left", Houellebecq an amoral kind of libertarian  they find that their shared vocation, their commitment to writers and writing, the self-sacrifice that has resulted, is a far more powerful ideological force. In an effort to explain the masochism of their media identities, they swap confession and scraps of autobiography, dwell in detail on the public scrutiny of their parentage, Houellebecq on the infamous betrayals of the mother who abandoned him to the temptations of the 60s, Lévy on the implications of being the son of a plutocrat industrialist (his old man was a self-made timber millionaire). Though aware that their exchanges will be eavesdropped by a readership in many languages, they maintain the epistolary conventions of intimacy, the illusion of private conspiracy. Perhaps surprisingly, it is a tone that sustains the flimsy premise they concocted over dinner.

Though Houellebecq can't resist the odd inflammatory aside  "Personally, I don't believe in Jews," he says at one point, after Lévy has been dwelling on the semitic persecution complex he may or may not have been born with  he finds himself exploring some emotions that have not always come easily to him as a novelist: kindness, say, and generosity of spirit. He'd probably hate to admit it, but Lévy appears to bring out the best in him.

Dropping his cynicism completely at one point, for example, he claims that he fully understands the philosopher's penchant for day trips to Darfur, the whistle-stop compassion tourism for which he receives a great deal of mockery in France. As a philosopher, Houellebecq often seems to dance quite easily around Lévy's stated positions, his progressive optimism, and not only because it is generally so much more persuasive to believe in nothing than in something. Though both men are alive to their limitations, Houellebecq emerges as the more interesting self-analyst: "Very few adults realise that every child, naturally, instinctively, is a philosopher," he says, for example. "It sometimes seems to me that as a man, all I have done is to give aesthetic expression to the withdrawal that as a child I witnessed in my father"

This is, as you may have already recognised, a very French book. It is hard to imagine a British equivalent  who would we end up with? Irvine Welsh and Alain de Botton? What keeps you reading, beyond the confessional drama, is the sheer one-upmanship in the range of reference and playfulness of expression. At one point, the sparring philosophers direct their attention to the future of the French economy: given its terminal decline as an industrial power, what are the nation's remaining world-class attributes? Duck confit, Houellebecq suggests, and romanesque churches and raw-milk cheese. To this list he might have added the original gift of the French enlightenment, the tradition of memorable after-dinner conversation, to which this volume is an exceptional, and enjoyable, addition.