No one could ever accuse Clare Denis’ film of being action-packed, but “35 Shots of Rum”—which on the surface might sound like something Guy Ritchie or Luc Besson would produce—proves to be a gently affecting study of the relationships among a group of friends and family. It’s a typically French slice-of-life film, which means that it’s concerned with subtle emotional undercurrents and complex character traits rather than obvious melodramatic explosions and big revelations.

The picture centers on a few residents in a Paris apartment building. One flat is occupied by Lionel (Alex Descas), a taciturn widowed subway-train driver, and his daughter Josephine (Mati Diop), a beautiful university student. The two are obviously devoted to one another, made evident not so much in words as in gestures and glances. An adjacent apartment belongs to Gabrielle (Nicole Dogue), a feisty cabdriver and former girlfriend of Lionel’s, who’s obviously still in love with him, and another is owned by Noe (Gregoire Colin), a young man who’s mourning the death of his parents, travels a lot and clearly has eyes for Josephine (as does one of her classmates).

Much of the film is made up of the close observation of these four, particularly in an extended sequence in which they head out to a concert, only to wind up in a café at closing hour after Gabrielle’s car breaks down. As Josephine dances with Noe, Lionel’s face shows a mixture of affection and concern; and as Lionel in turn takes to the floor with the place’s gorgeous owner (Adele Ado), Gabrielle’s exhibits simmering but unspoken envy. It’s a lovely scene which, like the picture as a whole, is mostly made up of small but telling details. Another plot thread, a bittersweet counterpoint to Lionel, focuses on his just-retired colleague Rene (Julieth Mars Toussaint), who finds himself alone and depressed in his new jobless state. It’s handled without exaggeration, too, as is a sequence toward the close in which Lionel and Josephine visit her aunt (Ingrid Caven) in Germany. In fact, the only scene in “35 Shots” that comes on too strong is one set in Josephine’s classroom, where the discussion is heavy-handedly academic. On the other hand, in general the film handles the multi-cultural, ethnically mixed reality of the characters and the society that surrounds them without comment, and when big events do occur—a death (whether of a human being or of a beloved cat) or a wedding—they’re actually underplayed.

Denis handles things with natural, unforced grace, and her cast responds with performances of quiet authority. Descas holds the screen effortlessly as a man genuinely frightened of losing his daughter while wanting to liberate her, and Diop draws a touching picture of a girl equally tied to her father yet moving toward womanhood. Dogue and Colin are similarly adept at conveying the characters’ emotions without overstatement, and Toussaint etches a moving portrait of a man lost without his work. On the technical side, the film is very simply and unaffectedly done, but the lack of glitz suits the material and Denis’ approach.

The title, incidentally, refers to a prodigious feat of alcohol consumption that Lionel and his buddies occasionally refer to but undertake only on the most special of occasions. One closes the picture, which is pretty special itself.