And then there were 15. Mia Farrow is standing in the middle of the dining room of Frog Hollow, her cottage in Connecticut, describing how she recently acquired a new member of her family. About 30 of her brood - many of her 14 children, several in-laws and a burgeoning generation of grandchildren - were crammed in around the dining table at one of their regular get-togethers.

They had had a "family talk", as Farrow puts it, about a woman in her late 20s who had recently become a friend and who had no real home of her own. "You know, we are the kind of family that is not united by anything as paltry as blood lines," Farrow says with an intense expression. "We are united by something so much more important: our mutual commitment and love. So we can decide who's in our family, and we all said we wanted her included, and we asked her, would you like to join us? And she said yes and every person in the family welcomed her."

It is anecdotes such as this that have given Farrow a reputation for being faintly batty. Who in their right mind would adopt 10 girls and boys, on top of her own four by two different men (André Previn, Woody Allen) - and then bring on board a 15th by family committee?

But look at it from where she's sitting - legs and arms folded, sipping a cup of hot chocolate by the window of Frog Hollow - and there is a logic to what she says that makes it all sound quite normal. The house overlooks a frozen pond where children used to skate before global warming thinned the ice. The interior is a riot of wooden beams and creaky floorboards, with shelves of books. One end of the sitting room has been converted into "grandchild corner", a jumble of dolls and fluffy toys. Two shaggy dogs and a cat complete the picture.

It is an idyll in the English country house mould, or as she describes it to me, an "extremely presumptuous dream" of family life. Yet in the middle of it sits, incongruously, one of the most famous actors of her generation, the woman who, alongside Twiggy, became the face of the 1960s, and whose name became a byword for Manhattan chic. She has been on a long journey, from her first husband Frank Sinatra's pad in Palm Springs, via the Maharishi's ashram in India with the Beatles, to this rustic shrine in the Connecticut hills.

These two sides of Farrow's life - film and family - come together in her latest work, Luc Besson's Arthur and the Invisibles, in which she plays a grandmother attempting to defend her rural home against the ravages of property developers. She jumped at the part, she says, even before she knew what it entailed, such was her admiration for the director of Léon and The Fifth Element.

The role Besson gives her is meagre compared to her great early work, in Rosemary's Baby and The Great Gatsby. Or Woody Allen parts such as Tina, the gangster's moll in Broadway Danny Rose. But she brings to the film her trademark charm, her still-youthful looks and that light sing-song voice that seems to have been formed somewhere in the mid-Atlantic. (She grew up in Los Angeles, but when she first started acting - in Peyton Place, in 1964 - the producer asked her whether she could do an American accent.)

Besson's film comes at a busy time for Farrow: a few years ago, she returned to Broadway, winning rave reviews as a dying woman in a new play, Fran's Bed. And she recently finished shooting a movie for Michel Gondry (director of Eternal Sunshine of the Spotless Mind), titled Be Kind Rewind, in which she stars opposite Jack Black. This summer she will begin filming the final two parts of an Arthur trilogy with Besson.

Farrow was born into movies. Her parents were Maureen O'Sullivan, who played Jane to Johnny Weissmuller's Tarzan, and the director John Farrow. The producer of Laurel and Hardy lived next door in Beverley Hills, and she went to nursery with Liza Minnelli. Theirs was an itinerant life, with movies taking the young Mia and her six siblings to Mexico, Spain, Ireland, England and New York. On top of that, there was a succession of personal crises: a bout of polio at age nine, the death of her brother Mike in a plane crash, and the alcohol-fuelled bickering of her parents. She once saw her father chase her mother through the house with a kitchen knife.

This was not, I suggest, a particularly stable childhood. She nurses her chocolate for a while, then says: "No. I don't really know what stability is. I don't really know that. I would like that, but I've never had that."

In the memoir she wrote a decade ago, What Falls Away, Farrow describes how at times in her childhood she felt utterly helpless, as though she were watching events unfold on television, unable to change the channel. Even so, a Hollywood childhood has its compensations. She remembers being scooped up by John Wayne when she was three, and the sense of awe she felt when visiting a set: "It had total wonder - the magic of it all. If I made a sound I could have brought the entire set down and terminated the whole shooting. With one shout I could make it all disappear."

She had an intensely religious, Catholic upbringing, a consequence of her mother's Irish roots and a father who was a convert - which, she says, "is even worse". After 13 years of Catholic education, draping statues at home with purple cloth at Lent, Farrow decided to become a Carmelite nun. "It was a fervent wish, even though I was riddled with doubt - I'm always riddled with doubt. I wanted the call, the vocation. I was sure I would get stigmata and that I would be lifted to heaven before I grew up. I was in another place entirely, where such things were possible."

If nothing else, it must have been a good training for acting, and there is something noticeably contemplative, almost meditative, about the way she has played many of her film roles. Maybe it's those enormous eyes: she once described herself as a pair of eyes on a stalk.

Far from enlisting in a nunnery, she ended up marrying Frank Sinatra at the age of 19; she says now she really didn't know what she was doing. "I was less mature than any other 19-year-old I've ever known. Poor Frank, saddled with such a child. I would be falling asleep at the table at Las Vegas, trying to talk to people about their cats. He was very patient with me."

Sinatra served divorce papers while she was filming Rosemary's Baby, aged 22, and she went on to marry, have twins and begin adopting Vietnamese war orphans with conductor and composer André Previn, before they, too, separated in an amicable divorce.

Then came the Woody Allen years: 13 films in 13 years, followed by one hell of a bang. So much has been written about Allen's affair with Farrow's adopted daughter, Soon-Yi, and the ensuing allegations of sexual abuse against another daughter, that Farrow is burnt out by the subject.

She says now that the mess of those days is behind her - "It's nowhere." Both Allen and his wife Soon-Yi are behind her, too, "to the extent that anyone ever can be who you have loved". She illustrates the point by talking about Allen in the impersonal form, blaming "someone" for portraying her as an eccentric at the time of the split, when "the person who was saying it knew otherwise or he certainly would not have spent 13 years together with me".

What she will not do - she is dogged on the subject - is allow the bitterness of the fall-out to cloud her judgment about the films they made together. "I felt, and I do feel, that that was a really wonderful run of films. I'm extremely grateful for those years. My kids were living in New York City with me and mum; Woody was right across the park. It was extremely romantic. And if the films didn't all turn out to be great, it was not because he didn't try. He had very high standards."

Rewatching some of those films, I can't help thinking that she sacrificed a huge chunk of her career by working with just one director - her partner, to boot. Take Crimes and Misdemeanours: a great, dark film but a completely unmemorable part for Farrow. But she is having none of it. "OK, my part was inconsequential and not at all satisfying, but it was his best film to date, quite chilling. And I was part of the rep group that made it - I was breastfeeding at the time - and that suited me just fine."

Farrow's approach to life is the opposite of the norm: she sees film-making as the fun part. Work begins as soon as she steps off the set, and her real job has been that of raising 14 children, who today span the ages of 36 to 12, including 10 adopted children, several of whom have disabilities. She doesn't want to make a big deal of this. "I don't mean to toot my horn," she says, more than once. "I'm as messed up as the next person. I'm just bumbling along."

For her, adoption has been a way of fulfilling a moral obligation. "At the time I felt, this is something I could do - bring someone into my life. If I had been better educated, maybe I might have seen other ways to address the suffering in the world, but this is all I knew."

She has no plans to adopt more children, she says, but has found a new focus for her energies in the humanitarian crisis in Darfur; she now spends much of her time writing comment articles and giving speeches. Around her neck is a trinket given to her by a holy man in a Darfur refugee camp, and she recounts the story of a woman she met called Halima, who was forced to watch as the Janjaweed butchered her baby. "I am in Full Metal Jacket. I absolutely will not allow myself to think that nothing can be done. There is no excuse for that."

Next week, Farrow will travel to East Chad, her fourth visit. Before she goes, her extended family will gather again in Frog Hollow to celebrate a crop of birthdays, one of them being Mia's 62nd. "Once in a while," she says, "I have a gift of looking at all the people assembled around the table and thinking: I had an extremely presumptuous dream, and it came true. How lucky am I?"