The intriguing story behind “Seberg” and the reliable talent of its lead actress, Kristen Stewart, promise greatness. But this biopic manages to squander both, reducing the film to a bland period piece with an irritating lack of focus.

Jean Seberg was an American actress best known for her role in a French film, the 1960 Jean-Luc Godard New Wave drama “Breathless.” But by the late 1960s, this film suggests, the bilingual performer was growing bored of acting and was enthralled with the activist politics of the era, particularly the Black Panthers. It made her a target of the FBI, which harassed her relentlessly. Given Stewart’s own move away from commercial Hollywood fare lately (“JT LeRoy,” “Personal Shopper”), it’s easy to see why she’d gravitate to the project.

On a transatlantic flight, Seberg offers to give up her first-class seats for Betty Shabazz, the widow of Malcolm X, and Hakim Jamal (Anthony Mackie), his cousin. The interaction leads to an affair between Seberg and Jamal, both of whom are married, and to her being surveilled by the FBI and shot at by Jamal’s wife (Zazie Beetz, awfully briefly).

Director Benedict Andrews (“Una”) slogs the film along at a languid pace, cutting between Seberg’s life and the FBI men tasked with following and, ultimately, publicly humiliating the actress as part of the agency’s COINTELPRO program of the ’60s and ’70s, dedicated to disrupting domestic political dissidence.

Vince Vaughn appears periodically as a short-tempered agent (though it’s hard to take him entirely seriously), while Jack O’Connell (“Unbroken”), as his partner, is more morally troubled by the agency’s treatment of Seberg — though not enough to stop it.

“Seberg” isn’t helped by its sometimes laughably uninspired screenplay. We’re told at the start that the actress was badly burned playing Joan of Arc in the 1957 Otto Preminger movie “Saint Joan,” which is later unsubtly echoed when someone warns her she’s “playing with fire.”

The government’s treatment of the iconic actress, who died young in an apparent suicide, is ripe for exploration on film — it’s too bad “Seberg,” despite Stewart’s best efforts, doesn’t do its namesake justice.