Sofia Coppola was a laughing stock at 19 following her disastrous casting in dad Francis's third Godfather epic. Who would have thought that the one-time punchline would reinvent herself as the critically acclaimed director of the zeigest-defining films The Virgin Suicides and Lost in Translation? Coppola is now 35 but still retains the 'whatever' air of a bored twenty-something, as Donald Clarke discovered while straining to hear her talk about her new film, Marie Antoinette

SOFIA Coppola, director of the bewitchingly ethereal Lost in Translation and, now, the airy, dreamlike Marie Antoinette, swaggers into the room and slaps me heartily on the back. She is wearing a pair of greasy cargo pants and, only occasionally visible through clouds of rancid cigar smoke, a black patch over her heavily bruised right eye. After extracting the cork from a bottle of cheap whiskey with her jagged teeth, she swills some of the pungent liquid into a dirty glass, knocks back an inch or two and begins shouting about politics and basketball.

I'm joking of course. You will never, I suspect, have encountered anybody quite as vague and psychologically diffuse as Sofia.

Curled up in such a way as to force as much of her body as possible into the angle of her comfy chair, she mumbles infuriatingly brief answers in a voice that begins at a gentle volume, before tapering off further until the words are barely comprehensible. Each sentence sounds as if it were delivered from the back seat of car driving slowly into the distance.

Coppola seems very nice, you understand. But she just doesn't appear to be interested in anything. For example, who better to ask about the still puzzling under-representation of women in the film industry than Sofia Coppola? She is, after all, still the only female American to be nominated for an Academy Award as best director.

"I was really surprised when they told me that," she murmurs. "I never really thought about it. I just want to make films and I make them. I don't really think about why more women aren't doing it."

But she must have done. How could she not have asked the question? "I don't know why it is. It is really not my place to discuss why there aren't more female directors. But I am glad when girls come up to me and tell me that I am an inspiration."

Let's try this from a personal angle. Bigots in more conventional industries have often suggested that women fail to succeed because they keep taking time off to have babies. Sofia, dressed today in soft neutral colours, is herself seven months' pregnant. What effect might the impending birth have on her career?

"I haven't thought much about it. But the good thing about film-making is that it's not like fashion. You don't have to produce new material every season." (She may have said something else on the subject, but, if so, her voice, overpowered by ambient hum and the noise of buses several miles distant, failed to register on my humble recording equipment.)

Two things strike me about Sofia's disarming introversion.

First, there's the eerie way she has insinuated that anaesthetised personality into her three features. The Virgin Suicides, Lost in Translation and Marie Antoinette all have a slightly deadened quality to them. This is not, in itself, meant as criticism. The first two films rate among the most entrancing American pictures of the last decade, and Marie Antoinette, though a tad one-note, offers the indulgent viewer copious pleasures. But Sofia's lethargic, barely conscious sensibility seeps through every frame of her work so far. The actors all seem slightly jet-lagged. (In Lost in Translation the characters were, of course, in just that state.) Nothing so troublesome as a plot disturbs the torpor. "I prefer to approach a film as if it were a poem rather than a story," she says.

The second point to note about the director's contained attitude concerns the striking contrast with her father's loud, overbearing enthusiasm for life's various pleasures. Francis Ford Coppola, director of The Godfather and Apocalypse Now, never whispers when he can bellow. Far from curling up in his seat, the vivacious Italian-American flings himself at interviewers and overpowers them with hand gestures. I have read that Francis told his daughter she would have to speak up a bit if she ever hoped to assert herself on set.

"He did say that when I was starting out," she says. "I think that cliche of the director being a dictator on set is not one I fit into. I don't feel the need to yell on set. As long as people are clear about what you want to do, then that's okay. If you want people to help you, then ask. And if they then don't, well . . . " The voice trails off, giving me some impression of the passive aggression that might greet any on-set insurgency.

Before she had spoken her first word, Sofia Coppola, born in 1971, had already appeared in one of the greatest films of all time. She was the child being christened in the iconic closing scenes of The Godfather. Her father, a great family man, made a point of transporting his children to each of his film sets. Sofia is characteristically verbose about her early experiences hanging around in the Philippines during the making of Apocalypse Now.

"I was so young, just four or five," she breathes. "That was just my dad going to work as far as I was concerned. I don't think I was really aware of what was going on. I was just having fun being in the jungle."

The young Coppola turned up in several more of her father's pictures, but had to wait until 1990 for critics to take note.

Unhappily the film in question was The Godfather Part III, for which Sofia, replacing an indisposed Winona Ryder in the role of Michael Corleone's daughter, received some of the worst reviews ever visited on any actor without the words "Rob" and "Schneider" in his or her name.

"It is hard when you are 18 and you are being told you ruined your father's movie," she says. "That isn't easy. But because I never really wanted to be an actress it didn't destroy my world or anything. My dad just asked me to do it and it seemed more fun than going back to college. At that stage of life, when you are already quite self-conscious, that sort of criticism is tricky. But that toughens you up."

Oh really. When Marie Antoinette, Coppola's meringue-light treatment of the last queen of France's adventures at Versailles, screened at Cannes earlier this year it is said some snootier members of the audience booed loudly. Was she tough enough to cope with that?

"Well, about four or five people booed and then came back and asked me what it was like to be booed. And in that way they made it news. The response was really good for the most part."

In the years following The Godfather III debacle, Sofia pursued a number of interests. She set up a fashion label. She dallied with still photography. Then, having messed around with cameras throughout her childhood, she became fixated on the notion of directing a film of Jeffrey Eugenides's appropriately vague novel The Virgin Suicides. Starring Kirsten Dunst (later to be Sofia's Marie Antoinette) the wistful film, a tale of angst from the suburbs, rapidly gathered a following.

Its successor, Lost in Translation, became, however, a genuine phenomenon on its release in 2003. Following Bill Murray's jet-lagged actor as he blearily accompanies Scarlett Johansson around Tokyo, Translation was nominated for four Oscars and has now established an unshakable position as a key artefact of its era.

While writing Lost in Translation, Coppola inserted a few apparently autobiographical nuggets that have bounced after her ever since. Johansson plays a confused girl from, it seems, a well-off background, who has spent the first years of adulthood dabbling in various art forms and fields of study. This sounds a little like a portrait of the director.

"Yeah, I was definitely writing about that period of being in your 20s when you don't know where to go," she says. "You try different things. I did spend time trying to work out what my calling was. I wanted to write about that."

More controversially, the film finds Johansson's character drifting away from the achingly trendy photographer she has recently married. Some months after the release of Lost in Translation, Sofia announced the break-up of her marriage to Spike Jonze, the, yes, achingly trendy director of Being John Malkovich and Adaptation.

"I was definitely looking at that stage of my life where I was living in a world that I wasn't relating to. You're married and find yourself in this strange world. You're trying to think how you fit into it."

So, is the pompous character played by Giovanni Ribisi a version of Spike? "No. But the film was a caricature of a lot of things in the world I was around then. I was making fun of some of that. You are snotty and 18 and you are not relating to a lot of the world that's around you."

Coppola, who, following an intriguing dalliance with Quentin Tarantino, is now seeing Thomas Mars, some class of French rock musician, cannot quite escape accusations of further autobiographical dabbling in Marie Antoinette. Based largely on Lady Antonia Fraser's study of the Austrian princess who married Louis XVI, didn't actually encourage the proles to eat cake and was eventually guillotined, the film, cut imaginatively to classic post-punk music, tells the story of a callow - though basically decent - young woman coming of age in an absurdly cossetted environment. Watching Dunst and her posh pals partying to the strains of New Order and Bow Wow Wow, it's hard not to think we are observing an excerpt from I Was a Teenage Coppola.

"I wanted it to be a personal story before anything else," she says. "It's a girl developing from a child into a woman. I didn't want to focus on politics. The idea of one group of people being so out of it and so unaware of what is going on elsewhere is relevant today. But I wasn't interested in making a political film. The emphasis is definitely on the personal element."

Coppola is consistently forgiving in her treatment of Marie Antoinette. In this regard, the film stays close to the spirit of Fraser's popular biography. Nonetheless, I imagine her ladyship, daughter of Lord Longford, wife of Harold Pinter, did not have The Gang of Four or Siouxsie and the Banshees in her mind when she was writing the book. So what on earth did the historian make of it?

"Oh, she really liked it," Coppola says. "I was really happy to hear that. She was a little surprised by the music, though. I remember sitting in a screening with her and listening to this Gang of Four track over the credits and thinking it was going on forever. I was dying for it to end. But, actually, she really liked the film and was really supportive. I got a nice letter from Harold Pinter as well and that is something to keep."

Following that exhausting, logistically complex shoot in the Palace of Versailles, Coppola, who has homes in New York and Paris, is looking forward to taking a year off to get to know her new baby. Then she intends to embark on a less cumbersome project, more obviously suited to her muted sensibility.

"I like more subtle performances," she muses. "Yeah, I guess I don't really like melodramatics. I like things a bit more subtle. I like things less operatic. I like focusing on all the things that are not spoken, rather than those that are said out loud."

So, what would she say to a fan who dared to suggest she might like to take a more robust attitude to plotting or character.

"Go and see somebody else's film."

Marie Antoinette goes on release next Friday