35 Shots of Rum, Claire Denis, 100 mins, (12A)

This gentle French drama gets under your skin with a heady cocktail of intimacy and family ties

French director Claire Denis has a reputation for difficulty – at least, for making wayward, elliptical films that take the circuitous route to get under your skin.

Her films tend to be fragmented, provisional-seeming, even her most provocative and forceful ones. Take Beau Travail: a Foreign Legion story mixing drama and dance, with a soundtrack of Benjamin Britten and Euro disco, and a central character borrowed from an early 1960s Godard film. Denis doesn't make films "about" subjects, nor does she go in for straight storytelling; rather, she gestures obliquely at everything that's been on her mind throughout the film-making, and if the results emerge as reveries, or enigmas, they're all the richer for it.

Even so, Denis's latest film, 35 Shots of Rum, appears comparatively simple – appears, mark you, and comparatively. Yet every shot is so sensuously vivid that even this family vignette lets you know that you're dealing with a film-maker of intense vision and stylistic subtlety.

Lionel (Alex Descas) is a middle-aged train driver on Paris's suburban RER network, Josephine (Mati Diop) a student – although it takes a while to emerge that they are father and daughter rather than a May-September couple. The film is about their life together – or, rather, about significant if quiet moments in their world. It's also about their friends and neighbours: taxi driver Gabrielle (Nicole Dogue), who has long been hopelessly in love with Lionel; and the bullish young Noé (Grégoire Colin), who drifts obscurely in and out of the role of Josephine's admirer.

The little that happens is a matter of event rather than narrative. Josephine attends a seminar on Third World debt, and Lionel attends a friend's retirement party, an occasion for the ritual – possibly his invention, possibly not – of downing 35 shots of rum. The pair also take a brief trip to Lübeck, to visit Josephine's German aunt. This is the film's only awkward passage, less in its abrupt unexpectedness than in the sheer oddity of former Fassbinder regular Ingrid Caven, whose histrionic archness is wildly out of sync with the rest.

The centrepiece sequence is the extended family's outing to a concert that they never reach because Gabrielle's cab breaks down. Stuck in a downpour, the company shelters in a café, where an impromptu dance party follows – Denis relishing, in its lush entirety, the Commodores' hit "Night Shift". The sequence is about pairings and looks: Lionel dances with Gabrielle, then with Josephine; he watches his daughter with Noé, before himself being scrutinised by Gabrielle as he takes a spin with the café's glamorous African owner. These exchanged glances – of worry, tenderness, jealousy – sketch out a concise essay on the way people feel, but don't always express, their closeness. By the time everyone takes the bus home, exhilarated and wrecked, you feel you've lived through the whole night with them, although the sequence lasts only minutes.

Denis, as usual, lets her actors fill the screen with their own idiosyncratic being. Alex Descas is one of a family of regulars who have grown older with Denis's films: here, he's a saturnine patriarch, his quiet masculine charisma saying everything about why Gabrielle loves Lionel. Another Denis acolyte, Grégoire Colin, has a wolfish presence as Noé, and a deliciously callous comic moment as he prosaically bids farewell to his dead cat by dumping it in a rubbish bag.

A new face, Mati Diop, illuminates Josephine's character without saying a great deal: her willowy beauty evokes delicacy, acute intelligence and a toughness that doesn't need to be spelled out. But the story's real centre is arguably Gabrielle: a stalwart friend who's probably destined to stay on the sidelines, and knows it. She might come across as a tragic figure, if not for Nicole Dogue, whose radiant smile carries an intense charge of indomitable character: Gabrielle's bantering with a fare, as lovers-rock reggae fills her cab, is one of those moments where a film miraculously, without fuss, catches the energy of everyday snatched pleasure.

Noé apart, all the film's characters are black, and mainly Caribbean, but Denis never makes a point of this. At moments, Caribbean identity becomes more specifically visible, as in a reference to radio station Tropiques FM, but it never defines these characters, certainly not in a way that limits the complexity that interests Denis – their complexity as Parisians, or students, or railway workers.

With more than a nod to Ozu, Denis concentrates on the ordinary details of domesticity – a pair of rice steamers, Lionel's habit of putting on his slippers. Unusually, this is a picture of home not as a claustrophobic place of trauma, but as a safe, nourishing haven – even if it won't be Josephine's home for ever.

Nevertheless, 35 Shots is steeped with melancholy and there's one moment of outright tragedy. And the film is still something of a jigsaw: a succession of passing moments and moods for us to assemble into a picture. There's also one moment that is wonderfully inscrutable in typical Denis fashion, as Lionel and Josephine gallop along a railway line on horseback: dream, metaphor or just a favourite recreation among RER employees and their families?

Denis's regular photographer Agnès Godard shoots with a fine eye for atmosphere, for the tactility of light. The score, with its wispy fairground waltzes, is by British band Tindersticks. In its distracted, undemonstrative way, 35 Shots of Rum is as heady as its title suggests, quietly crackling with intimacy and intensity.

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