Gérard Depardieu's striptease takes place in a tent on the beach, cunningly disguised as a motion picture premiere. There on screen, the ageing bull of French cinema literally and metaphorically exposes himself, turning left and right to show the ravages of time. Depardieu looks like hell and the Cannes film festival audience is in uproar. Each drag of his belly is accompanied by disbelieving hoots and embarrassed guffaws. The audience can't decide whether it's witnessing the death throes of a legend or the convulsive birth of a new kind of screen nudity.

Apologies to the aesthetes, but naked bodies sell movies. It's a truism that goes right back to film's disreputable beginnings as a peep-show at the circus. It's the unspoken contract at the heart of arthouse cinema, with its habit of employing perky gamines to sweeten challenging drama. But now the old model is breaking down, outstripped by the new flesh of sagging torsos and dangling genitalia – what some describe as "horror nudity" and others as a different kind of beauty. The future is mottled; it has a gut and grey hair. And as with most things, we have the internet to blame.

Sight and Sound editor Nick James remembers the way things used to be. "You had a whole generation of teenagers who would flock to see a bit of softcore nudity in an arthouse film," he says. "It was part of their education; I did it myself. It's probably one of the reasons why I have my job today."

Now, by contrast, softcore and hardcore are just a mouse click away. "The whole image of bohemianism in the arts was that it involved a freer attitude towards nudity and sex," says James. "But that's been undermined by the free availability of porn. The people who like that sort of thing are now better served elsewhere." The film-makers, then, have had to adapt to survive.

Directed by Abel Ferrara, Welcome to New York casts Depardieu as a thinly veiled Dominique Strauss-Kahn, the disgraced former boss of the IMF, arrested for his reported sexual assault of a hotel housemaid. It's a movie that installs the 65-year-old actor as the bloated, corrupted symbol of a bloated, corrupted body politic; a film that uses nakedness not to excite but to disturb. File it alongside Lars von Trier's Nymphomaniac, Julia Leigh's Sleeping Beauty and the work of the Mexican director Carlos Reygadas, with its obese lovers and lolling bath-house tableaux. These films have no interest in liberation and fun. Instead, they frame sex as something hazardous, sometimes abusive and possibly pathological, with on-screen nudity its loose, hairy canvas. All at once the traditional, decorative nudity of a film such as François Ozon's Jeune et Jolie feels very tame and old hat.

"Of course you still have films full of glamourised, fabricated, Photoshopped nudity," explains the French writer Agnès Poirier. "But, on the other hand, you are seeing those that show life taking its toll on the flesh. These are films about the decay of the body, the decay of desire. So there is not the titillation there used to be. You could even say that nudity is the new horror. There is a quote from the poet Stéphane Mallarmé: 'La chair est triste', the flesh is sad. That's what cinema is about these days."

In Cannes, after the premiere, Depardieu was tickled by the suggestion he had made a pornographic movie. Welcome to New York, he insisted, did not quite measure up. "It's not porno at all," he said. "In porno you have to see the big dick." His argument is echoed by the Swedish actor Stellan Skarsgård, who gloomily unzips himself in the final scene of Nymphomaniac. "Pornography has just one purpose, which is to arouse you," Skarsgård told me recently. "But if you look at this film, it's actually a really bad porn movie, even if you fast-forward." Or to put it another way: directors such as Ferrara and von Trier take the hallmarks of porn and use them to trip us up, twisting the glamour into anti-glamour. And if the viewer is shocked, then so much the better.

"For anyone who encountered Depardieu when he was young, svelte and gorgeous, his current incarnation has to be viewed as a physical tragedy," says James. "It was impossible then to imagine how he would turn out, that awful self-creation. But our revulsion – if we assume we are revolted – is at least partly down to social conditioning." And there's the rub. Because if beauty is in the eye of the beholder, then our reaction to a film such as Welcome to New York or Sleeping Beauty says as much about us as it does about the film-makers. Have audiences been so conditioned by decades of prettified, fantasy nudity that the sight of an older body has become automatically shocking? And yes, no doubt they have been. But that's not the whole picture. Alongside Depardieu's striptease, for instance, the Cannes organisers also found room for Olivier Assayas's backstage melodrama Clouds of Sils Maria, which features a scene in which 50-year-old Juliette Binoche bathes naked in a mountain lake. Tellingly, this moment was not presented as transgressive, or even out of the ordinary. It was taken as read that we would see Binoche as being just as natural – and just as beautiful – as Kristen Stewart, her 24-year-old co-star.

But Depardieu comes with a different intent. In scene after scene, he parades his body as a map of debauchery, counting the cost of decades of drinking, eating and smoking (with a brief – and perhaps inevitable – pause for quintuple bypass surgery). Some may see this as the last gasp of a dying animal. The actor, after all, claims he "doesn't give a shit about cinema any more". He has fled the French tax laws to cosy up to Putin. His daughter reportedly gives him another five years to live. And yet when we watch him in Welcome to New York, we recall him in his younger, fresher days, cavorting with Miou-Miou in Les Valseuses, or coaxing Robert De Niro through a threesome in Bertolucci's 1900. The man has grown old alongside the art-house; its thrusting young buck turned jaundiced emperor. All of which makes him the perfect model for this new breed of sad flesh, this fresh twist on art cinema. He looks, paradoxically, more vital and significant than he has done in years.

According to Poirier, Depardieu is the great ogre of French cinema – a man who grew too big for the movies and couldn't give a damn about the way he is perceived. "I am sure he would say that he doesn't care what people think of him. He doesn't care what he looks like, or how people react. But that's easy to say, and I wonder if it's true. No one is immune to the spectacle of their own decay. It takes a very brave and intelligent actor to be able to confront that head on." And if Depardieu can do it, we surely should, too. So enough with the hooting and the embarrassed guffaws. Depardieu points the way forward and leaves us all playing catch-up.

• Welcome to New York is released in cinemas and available on demand on 8 August. Own it on Blu-Ray and DVD from 29 September.