Sofia Coppola was five years old in 1977 when her father, Francis Ford — fresh off the wild shoot for Apocalypse Now — interviewed her. “I’m a little fishy, and I swim in the water and have two brothers who are fishies,” she said, before counting in Cantonese. Later, father asked daughter to record a message for her future self. “I am Sofia,” she said. “And when I grow up I want to be a teacher or a nurse. I like being Sofia, because there’s a lot of fun things that I know how to do.”

Forty-three years later Coppola is on a Zoom call from Napa in California, where her family is and where she grew up. “Oh my God,” she says, reminded of the recording. “Yes, my dad interviewed me when I was a little kid.” The extended family have been together for lockdown — her husband, Thomas Mars; daughters Romy and Cosima; brother Roman — one of the “fishies” — with his children too. “It’s been OK,” she says. “Our kids are a little older, 10 and 13. But it’s hard for a teenager stuck at home with us.” She is in shirt and specs, in a room that looks like it’s waiting to be decorated. Lively chat fills rooms off-camera. It is in Napa that her father makes his wine, including the Sofia Chardonnay. “Light in spirit. Elegant in character,” the website reads.

“They think of me as … the daughter of the Godfather maker,” says Sofia Coppola, here on the set of The Godfather: Part II in 1974.

So what would Coppola say to her older self today? “Oh, trippy,” she says. She is 49. “I hope that I enjoyed it?” She laughs and adds that she just feels lucky she puts films out into the world that people, hopefully, get something from. It’s not teaching or nursing, then, but film-making is a fun thing she clearly knows how to do.

“Yes,” she nods. “So I guess I still feel the same as my five-year-old essence.” She had a strange upbringing. Her Oscar-winning father also filmed her birth. “I haven’t seen that in a long time,” says Coppola, now an Oscar winner too.

For her new film, On the Rocks, Coppola has — in a way — turned the camera back on Coppola Sr, and got Bill Murray to play him. As usual she writes and directs the story of Laura (Rashida Jones) and her dad, Felix (Murray), who spy on Laura’s husband, Dean (Marlon Wayans), when she suspects he might be cheating. It is part odd-couple caper, part moving look at that tricky time when children arrive and dreams are adjusted. “What if we find out he’s just busy?” Laura asks, as she and Felix snoop on Dean. “And I’m in a rut?”

Laura is Coppola’s alter ego. They even look alike. Dean goes away a lot, which makes Laura worry, and Coppola’s husband goes away a lot too, given that he is the singer in the globe-trotting French indie pop band Phoenix. “No,” Coppola says, when asked the obvious. “Their relationship is not based on mine. I was never paranoid and spying.” She heard a story like the one in the film from a friend, although the influence of Francis Ford throughout is very real.

“I just thought I’d love to see a father and daughter buddy story,” she says. “Because, of course, I have so many memories and quotes from my dad, and that relationship was really impactful on me. Felix is made up, yet there are elements of my dad. He was bigger than life to me growing up. But Felix is this international playboy, so he’s a combination of my dad and my dad’s friends. Also, my father-in-law is a fun big character. It is a bunch of figures in my life from that generation.”

A director and her muses: Sofia Coppola with Bill Murray and Francis Ford Coppola at the 2015 Marrakech Film Festival.

The conversations between father and daughter are blunt. It is like Curb Your Enthusiasm with a soul. “Women are the most beautiful between the ages of 35 and 39,” Felix says. “I have many months left,” Laura replies. This, incidentally, shows Coppola’s underrated humor. “People don’t think of me as funny,” she beams. “They think of me as a serious person and the daughter of the Godfathermaker — my humor is subtle.” At another point Laura asks Felix if a man can be satisfied with one woman, and the answer is far from reassuring.

“Felix is this international playboy,” says Coppola. “So he’s a combination of my dad and my dad’s friends.”

“I wanted to do something about men and women and different generations, because it has changed so much,” Coppola says. “There has been a big jump regarding the roles of women.” In terms of what? “Well, just in our culture there have been conversations about how men talk about women and relate to them. I’m not going to say it, but you know.”

I assume she means the Me Too movement. “It’s been a big conversation over the last couple of years about what’s appropriate and what isn’t, and I was trying to have Laura talk to Felix about it. There is a huge generational divide between men of my father’s generation and our generation. It had been on my mind for a while.”

It is her most personal film for years; the closest we have come to who Coppola is since Lost in Translation. Casting Murray, who revived his career with his role in that film, is coincidence, but that breakthrough of hers was essentially about her life then; unsure of her marriage, looking for connection in a foreign hotel bar, Scarlett Johansson as her younger alter ego.

That film was, she has said, a “really self-indulgent, personal project” — and that exposure scared her. Is she scared again? “Yes, but that comes with anything that you put out. It reveals what you are vulnerable about.”

If Coppola’s first film, The Virgin Suicides, was made because, as she said, she wanted to write for teenage girls, who is On the Rocks for? “I was making something about what my friends and I think about. It seems boring to make a film about middle-aged life, as there’s nothing glamorous about that, but I hope it connects for women going through what I was thinking.”

Murray and Rashida Jones in On the Rocks. “I wanted to do something about men and women and different generations, because it has changed so much,” Coppola says.

Specifically, she means those years just after having children. And in On the Rocks she gets the minutiae so well. There are the chats at school drop-off with parents you don’t like but pretend are interesting. There is a lot of Jones pushing a buggy around New York that looks like paparazzi shots of Coppola doing the same. A gorgeous scene in Mexico has Jones in a yellow dress in front of a pink wall, bringing to mind Frida Kahlo; but Coppola remains the big-screen director who most faithfully captures the mood of Edward Hopper’s Nighthawks in her work — all that silent woe.

One great moment has Laura going to Dean’s office. Laura is introduced as Dean’s wife, and there is awkwardness. Is it because everyone there is having sex with her husband, or just because they are younger than Laura?

“There’s a moment,” Coppola says, “when you have little kids and you’re working and thinking, ‘Who are you?’ You get lost in the shuffle, and then you find your way. I don’t feel like that now, but there was a moment I had to figure it out. As a writer I used to stay up all night, but when you have kids you can’t. As a writer you need hours to daydream. Then, suddenly, it’s ‘babysitter for two hours — be creative!’ It was a whole different shift.”

Coppola remains the big-screen director who most faithfully captures the mood of Edward Hopper’s Nighthawks in her work — all that silent woe.

This is Coppola’s role; she chronicles life’s disaffected, but not in any grand societal or politic way. Indeed, when asked about the lack of Oscar recognition for female directors, she says she doesn’t have an answer and decides not to engage. Most other female directors I have spoken to are the opposite. Maybe being born into the bigger picture allows one to ignore it and concentrate on the details instead, and it is in those details that her films come to life.

Even the sorely undervalued Marie Antoinette, starring Kirsten Dunst, fits that pattern. It emphasises character over history to come up with an in-depth look at a monarch as nuanced as The Crown.

That was the punk film of her career — about youth and rebellion. On the Rocks, on the other hand, is about the end of such abandon. “It does sound dull!” Coppola laughs, when describing her own movie. She is good company. Friendly, quiet, thoughtful. But it isn’t dull. It is more factual than anything; the rhythm of life. Because Coppola doesn’t really do downbeat — she just does accurate.

Towards the end of On the Rocks, Felix, with his big international life, looks at Laura, who largely stays at home, and says: “You have your own adventure.” It’s sweet. She was worried, but he is saying don’t be — your life is great, enjoy it. That is, I suppose, what we all have to learn, perhaps Coppola more than most. “For me,” she says. “It’s not so much about growing up, but about her finding her role outside of this big father character. And her role in her life.”

On the Rocks is in theaters beginning October 2 and on Apple TV+ beginning October 23

Jonathan Dean is a writer for The Sunday Times and the author of I Must Belong Somewhere: Three Men. Two Migrations. One Endless Journey