Jodie Foster is such a trustworthy actor, so intelligent about her credibility, that she can lead a patchwork French mystery-drama like “A Private Life” — which boasts the Academy Award winner’s Franco-fluency — as if it were simultaneously a wink at her celebrity, a perfect showcase for her talent and a handsome mess fortunate to have her imprimatur. In a way that makes her an ideal French movie star: a special brand of high wattage (Deneuve, Huppert, Binoche) that imbues just the right amount of class to an undercooked piece of adult peekaboo, while still burnishing the actor’s reputation.

Filmmaker Rebecca Zlotowski, whose last film was the heartfelt, complicated “Other People’s Children,” does well to cast Foster as American-born, Paris-based psychiatrist Lilian Steiner. It isn’t long after meeting Lilian in her well-appointed apartment/office, alone on a rainy night, bristling at her upstairs neighbors’ loud music and leaving a brusque voicemail for an absentee patient, that we sense this control-minded professional is in for some destabilizing. And knowing this is in Foster’s hands comes as close to a guarantee of quality as a movie can offer.

The swerve comes when Lilian learns that the absentee client — a beautiful, troubled woman named Paula (Virginie Efira, seen in flashbacks) — died suddenly. After being thrown out of the family’s shiva by widower Simon (Mathieu Amalric), but clinging to cryptic messages from the daughter (Luana Bajrami), Lilian suspects foul play rather than the official ruling of suicide. She even wrangles her affable ex-husband, Gaby (Daniel Auteuil), an eye doctor she’s still on good terms with, for investigative support.

It’s debatable, however, whether Lilian is on to something or just scrambling to make sense of a tragedy to assuage her own guilt, a question that rattles in our ears with every campy symphonic flourish or percussive ornamentation in the aggressive musical score. Zlotowski, working again with co-screenwriter Anne Berest and ultra-capable cinematographer George Lechaptois, doesn’t go for half-measures, so when Lilian sets aside her skepticism to look into things with a suspicious hypnotist, it comes complete with a red-hued Freudian dream sequence that convinces this tightly wound, coldly reasoned doctor to believe in the florid logic of past lives. It’s a change that comes as a surprise to her grown son (a wry Vincent Lacoste) who’s always had to accommodate a carefully distanced mom.

As “A Private Life” moves along, with Lilian negotiating a break-in, threats and lapses in judgment, it never exactly coheres. Yet it somehow entertains, which is a testament to Zlotowski’s energy juggling her various theme-colored story balls. While the mystery plot strains to be interesting as a lesson for its protagonist about how one never can fully know another human being, Lilian’s and Gaby’s rekindled affection is a wonderfully mature strand of midlife complexity, with Auteuil and Foster giving all their scenes the kind of nuanced, lived-in humor that suggests a flinty couple who never fully believed they were done with each other.

The slouchless cast also includes icons Irène Jacob and Aurore Clément, “Return to Seoul” breakout Park Ji-Min and documentary legend Frederick Wiseman (as Lilian’s mentor), but all in bits that range from stunty to blink-and-you’ll-miss-them. Again, the party seems like it was fun, and Foster attracts a deserving cohort for her first all-French-speaking role since 2004’s “A Very Long Engagement.” But it also leaves one realizing that “A Private Life,” despite the commanding leading lady holding its center, is a bit mixed up by design.