Jason Schwartzman didn’t start in the family firm. When he was 17 he was cast as the lead in Rushmore, Wes Anderson’s breakthrough feature about a self-important schoolboy with an inappropriate crush. It remains his best-known film, widely beloved. He has now made seven films with Anderson, including playing a recently widowed war photographer in Asteroid City. That’s his gang.

By comparison, the fact that he is a Coppola – his mother is Francis Ford Coppola’s sister – is merely a point of interest. Even when he played Louis XVI in Sofia Coppola’s Marie Antoinette, the most striking thing about seeing him in his cousin’s film was what a wacky, perfect casting choice it was.

Anyway, if there is even a bit of “nepo baby” in there, Schwartzman is the most self-effacing nepo star on the planet. When he goes to a set, he said recently, he worries whether he can make it worth the bother of leaving their families for the other cast members. And he never suggests the other Coppolas should come and see his work, even though he’s always eager to see theirs. “I could say almost the opposite: ‘please, don’t watch anything’. I don’t like the imposition.”

But you have to hope that Coppolas Francis, Sofia and Roman, and Nicolas Cage – the whole gang – were queuing in Sundance to see Between the Temples, in which Schwartzman plays a troubled cantor at a (very liberal) Reform synagogue.

Following his wife’s death, Schwartzman’s Ben Gottlieb has found himself unable to sing, which is the cantor’s job. Rabbi Bruce (Robert Smigel) keeps him on, partly because he teaches the preparatory bar and bat mitzvah class, partly in the hope Ben will be a suitable match for his neurotic daughter Gabby (Madeline Weinstein).

There are many familiar tropes of Jewish comedy in this film – dominant mothers (two of them, in fact: a lesbian couple made up of scary Dolly de Leon and Caroline Aaron), awkward matchmaking and the inevitably excruciating Friday-night dinners.

Nathan Silver’s film gives all the cliches fresh life, however; the film was based on a 20-page “scriptment” and largely improvised, after which the cast argued for what should be included and in what order. The resulting film rolls energetically between its foundations in tragedy and a light-hearted catalogue of human follies. At the same time it pushes a big envelope.

Ben’s life starts to turn around – and everyone else’s life goes into a tailspin as a result – when he is reunited with his grade-school music teacher in a dive bar where he has managed to pick a fight. Carla O’Connor picks him up from the floor and puts ice blocks on his cut head, while telling him she is actually Jewish – nee Kessler – but that because her parents were staunchly secular and her husband Catholic she never had a bat mitzvah.

A few days later she turns up at the temple, asking for the rite of passage she missed as a child. He starts teaching her Hebrew, whereupon a relationship develops that is decidedly, if chastely, romantic. Ben is said to be 40; Carla is played by Carol Kane, whose first great film role was in Joan Micklin Silver’s Hester Street back in 1975.

Kane is 72 in real life, with eyes that are a little milky, a slightly quavering voice and – as Carla, at least – the ramshackle, ditzy charm of someone who doesn’t care. It could be twee; it could be, frankly, very weird. Silver makes it genuine and sweet, even while running up against one of the last sexual taboos.

Schwartzman says he didn’t give any thought to their age gap. “The way I thought about it, my character is in mourning and in grief,” he says. “This is going out on a crazy limb here, but she is all the things that he can’t be right now: more wild and free. Oftentimes, that’s what you look for in a partner. There is also something there about death that is connected to her in some way that is attractive, connected to his mourning. But taboos? I didn’t think about it.”

He had other kinds of questions. His father, the actor and film producer Jack Schwartzman, was Jewish; his mother, Talia Shire, Oscar-nominated star of both Rocky and her brother Francis Ford Coppola’s The Godfather, was raised Catholic. When Heeb magazine (a hipster Jewish mag based in Brooklyn) asked him about being half-Jewish, he said he felt he was everything. “I am everything and nothing at the same time,” he said. “I’m proud to be Jewish, but I’m just lucky to be here.”

Like Carla, he learnt a good deal about Judaism from debating it on Between the Temples. “I think, for me, there were two things I took to heart deeply,” he says now. “One, the music of Judaism has become a big thing [for me].” Schwartzman is a prolific actor, but he has a previous career as a drummer and songwriter with Phantom Planet. Learning the cadences and songs and the chants has really been beautiful.

“Also, what we kept discovering with Nathan is that there are so many different sects of Judaism, so many different answers. As we were making the film I’d write down all my questions, and every time I asked them I would get different answers. And I found that seems to be one of the fundamental feelings or pillars of Judaism is the questioning and argument that follows. I found that really interesting.”

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What has he discovered through his career as an actor? He looks bemused.

“I don’t know what I’m discovering. Honestly – and this is not a new answer – anyone would say the more you do something, the sense of gratitude is more and more powerful.

“But I also feel more and more nervous as the years go on, too. Because it doesn’t make you feel more solid, it’s more like, ‘they’re really gonna find out now’.

“But, I don’t know, for me it’s a sense of gratitude. I know it’s a cheesy answer, but I’m going with it.”

Between the Temples screens as part of the Jewish International Film Festival (runs until December 22).

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