It rains overnight and the next day Cannes feels as though it's been out at sea. Everything is drenched and dripping; I half expect to see fish expiring on the steps of the Palais. On the rooftop terrace of an adjacent hotel, the plastic sheeting billows like a mainsail, and there in the corner sits Francis Ford Coppola, the ancient mariner of American cinema himself, blown back from obscurity. He says he needs a coffee to perk him up.

Coppola first came to Cannes in 1969 - with a film called The Rain People, strangely enough - and remains one of the few directors to win the festival's top prize twice: for The Conversation in 1974, and for Apocalypse Now in 1979. Today, with his white beard and bright pink socks, he has the look of a tourist letting his hair down on a summer vacation. Where did the time go, he wonders. "I've been in this business for more than 40 years. It feels like two."

The film festival originally offered him an out-of-competition slot for his latest film - an exalted but largely meaningless honour - and he turned them down. Instead, he has opted to compete in the Directors' Fortnight, where he looms like a giant among the less familiar names. Yet, this is somehow fitting, because his low-budget, black-and-white, entirely self-financed Tetro looks for all the world like the work of a first- or second-time film-maker. It is, he says, the sort of film he always wanted to make, before events dragged him off in a different direction. After a 10-year hiatus starting in the mid-1990s, Coppola is back behind the camera - first with 2007's Youth Without Youth, and now this one. "I'm like a retired businessman," he says. "But rather than play golf, I've decided to make art films instead."

Age, he says, has brought a new perspective. He is done with the critics, and done with the studios. He is not worried about ruining his career, because he doesn't have a career to ruin. "I know people say, 'Well, these films aren't as good as the ones he made earlier.' But you have to remember that those were bad movies, too. Read the first reviews of Apocalypse Now! Read the Variety review of The Godfather! They said it was boring, and dark, and pretentious. So it's funny. It's like I'm competing with this version of myself from a time when they didn't like me anyway."

It's true that Tetro has had mixed reviews since its premiere last Thursday night, but it worked for me. Luxuriating in the sights and sounds of Buenos Aires, the film follows the attempts of a callow young sailor (Alden Ehrenreich) to forge a relationship with his estranged elder brother (Vincent Gallo). It is a ripe, expressionistic family saga; a film half-drunk on high emotion and fantastical set-pieces. It's so clearly born out of passion that you forgive its occasional cornball digressions.

Coppola's coffee arrives and he sits cradling it to his kingly paunch. He is preoccupied with this idea of criticism. It can hurt, he says, because it gets delivered from on high and makes no distinction between the art and the artist. He admits this is something he sometimes struggles with himself. "It's like me with Picasso. His work is very clever and impressive, but he was a terrible person. He was a bad father and a bad husband. So I have a hard time admiring his work, because I know he wasn't good to his kids."

When he started out, Coppola says, his plan was to be a writer-director of small-scale, personal projects. Except that, at the age of 30, he won an Oscar for writing the war movie Patton and was carried away by the tide. This sounds suspiciously close to a repudiation of pretty much everything he has done. God forbid that he is disowning the films that made him great?

"Well, when I was offered The Godfather, it was so surprising: I was so young. It was offered to a lot of very important directors - Elia Kazan, Costa-Gavras - and I was at the bottom of the barrel. I only got it because I was young and cheap, and was known as a writer, and they figured I could rewrite this terrible script they had. Oh, and also because I was Italian." He shakes his head. "The Godfather was an accident. But then it turned out to be so successful, despite the Variety review - that was a blow, my worst nightmare. I'd never had money before, and all at once I had money and esteem and the car and the house, and I went on a different trip to the one I intended. And then everything I did was trying to get back. When I made Apocalypse Now, the idea was to make a big, successful war film like A Bridge Too Far and then use the money to make smaller pictures. That was always the idea. That was what we were all going to do. Even George [Lucas], when he made Star Wars. Star Wars was not what he wanted."

In the early 1970s, Coppola was the leading light in a generation of movie brats who turned the Hollywood studio system on its head. He reframed the American experience through a more radical European style - but where Robert Altman was free-form, and Martin Scorsese wired, Coppola's films were brooding and measured, characterised by hushed conversations and sudden rips of violence. Along with Lucas, William Friedkin and others, these directors proved it was possible to make serious, artistic pictures within the studio system. Except that then Lucas - Coppola's one-time protege - took on the role of Judas. Star Wars wrecked the dream, sending Hollywood down the mega-budget, blockbuster route and casting Coppola out into the wilderness.

Coppola winces; he thinks this is too harsh a judgment. "But success can be very intoxicating," he says. "Particularly when you didn't plan it. It's like you're working in a coal mine and all of a sudden you become prime minister. Well, gee, OK, it's good to be king. The truth of the matter is that I was a few years older than George and Marty [Scorsese], so I was able to help them. But then you get seduced. And when you become successful, it becomes harder to go back and do the things you said you were going to do. So I'm still waiting for George to make his personal films, because you would be shocked at how talented he is."

As for Coppola, a certain bullheaded-ness and spendthrift nature proved his undoing. He went "insane" (his word) in the jungle while shooting Apocalypse Now, ran up such debts with his ambitious Zoetrope studios (as well as with gargantuan flops One from the Heart and The Cotton Club) that by the late 1980s he was forced to work as a hack for hire. "I had to make a payment every year, so I had to make a movie every year," he sighs. "That was a tough time for me."

Is Tetro a more personal film than, say, The Godfather, Rumble Fish or The Conversation? All share the same sombre texture, the same themes of loyalty and betrayal, ambition and corruption. But Coppola says Tetro is his most explicitly autobiographical film - a reimagined photo album that probes his relationship with his adored older brother, August (father of Nicolas Cage), who avoided the limelight and pursued a career in academia.

"Well, this film is obviously tackling some demons in my own family," he says. "You know families - you love all these people, but you hate them. But you love them. It's a very cloudy situation. But making a film like this was like asking a question and receiving some kind of answer. I learned some things about myself that I didn't know before. I didn't know that I felt abandoned by my brother. My brother was so good to me." He chuckles. "I'm 70 years old and I'm only finding this stuff out now.

"A couple of years ago I realised something," Coppola continues. "I realised that my time was running out. So now, because of my other activities, I'm in a position to concentrate on cinema and to make movies that are entirely independent of the companies that control the movies."

Besides, he says, he finds that film-making keeps him young. Cinema is such a youthful art that it makes children of us all. There is still so much more to discover; so many places to travel. "Sitting here talking to you," he says. "I feel as though the future is a clean sheet of paper".