Jodie Foster, flashing a broad smile, embraced director Rebecca Zlotowski at the Cannes Film Festival on Tuesday night as “Vie Privée” scored an impressive eight-minute standing ovation. The crowd cheered wildly for Foster even as the actress kept gesturing towards Zlotowski, as if reminding the audience that this was the filmmaker’s moment to bask in the applause. “Vie Privée” is an off-beat mystery about a psychotherapist who becomes convinced that her patient’s suicide was actually a murder — think of it as “Only Murders in the Building” with a dose of ennui.

The crowd for the film was certainly star-studded, a sign of the esteem in which Foster is held. Gael García Bernal and Alejandro González Iñárritu posed for pictures before the screening, while Scarlett Johansson strode the red carpet with her husband, Colin Jost. Johansson was accompanied by June Squibb, the 95-year-old star of her feature directorial debut,...