“Who is Jean Seberg?” a reporter asks the eponymous movie star midway through “Seberg,” attempting to close a puffy promotional interview for “Paint Your Wagon” with some semblance of personal insight. She doesn’t get to answer, as Seberg’s publicist swiftly calls time on the question: “Let’s just keep it about the movie,” he instructs. It’s one of many moments in Benedict Andrews’ slick, diverting portrait in which Seberg is shown to be treated as a product, a pawn or a patsy, handled by men in their own best interests rather than hers. And yet “Seberg” does something a little similar to that protective publicist: Every time it threatens to truly pierce the psyche of its subject, played with typically intriguing, elusory intelligence by Kristen Stewart, the more ordinary mechanics of the movie she’s serving get in the way.

In fairness, those mechanics are more movie-ish than anything the lives of most biopic subjects can muster: “Seberg” covers the years when the French-adopted American star was made a prime target of the FBI’s illegal COINTELPRO project, which took invasive and threatening measures to “neutralize” her support for the Black Panther movement in the late 1960s. It’s a hell of story, buffeting what ought to be a hell of a character study, yet a workmanlike script by Joe Shrapnel and Anna Waterhouse (“The Aftermath,” “Race”) doesn’t quite do either of these justice. Fiery political complexities of the era are ironed smooth, as are Seberg’s own fractured psychological impulses, while at least half the narrative is framed through the eyes of a fictional character — a flatly drawn, conscience-plagued federal agent, valiantly played by Jack O’Connell — considerably less interesting than the one we’ve turned up to see.

If it’s never less than proficient, that still makes “Seberg” a slight disappointment from celebrated stage director Andrews, whose undervalued debut feature “Una” adapted David Harrower’s “Blackbird” with eerie, formally resourceful elan. In its best scenes, the new film reaches for the cracked, melancholic derangement of Pablo Larrain’s icon study “Jackie” — not coincidentally, those tend to be the scenes that let Stewart’s emotive furled fist of a face, rather than the frequently on-the-nose dialogue, silently do the talking.

The opening shot promises something more brazenly stylized altogether, as Andrews and d.p. Rachel Morrison recreate (in velvety color, rather than the original monochrome) the execution scene from Otto Preminger’s 1957 scene “Saint Joan”: Pixie-cropped and stake-tied, Stewart’s then 18-year-old Joan of Arc is set alight, flames drowning out her anxious amplified breathing on the soundtrack. It was Seberg’s ill-received screen debut, leaving her burned in more ways than one by the Hollywood patriarchy; in “Seberg,” furthermore, the scene symbolically casts her as a martyr from the get-go, punished for her steadfast convictions.

Cut to 1968, where Seberg — now Paris-based and married to French novelist and filmmaker Romain Gary (Yvan Attal) — is attempting a Hollywood comeback. Though she’s impervious to the May riots raging in her chosen home city, her politics slip out to her agent’s dismay when she befriends charismatic Black Power activist Hakim Jamal (Anthony Mackie) on the flight over; joining the Panthers in a posed salute at the airport, her French-vanilla hair and butter-yellow sundress sticking out like an unsore thumb against the others, she creates a photo op with increasingly severe consequences.

Seberg’s Hollywood liberal credentials are well-established — she proudly boasts of being an NAACP member from the age of 14 — and it isn’t long before she’s making donations to the Black Panther Party, hosting events for them at her glassy Los Angeles mansion and sleeping with Hakim, all of which combine to make her a person of interest to the Feds. Jack Solomon (O’Connell), a wet-behind-the-ears FBI recruit specializing in sound technology, is hired to bug Seberg’s home and lead a surveillance team with bigoted veteran Kowalski (Vince Vaughn, seemingly Hollywood’s new go-to guy for aggressive right-wingers). Yet the more supposedly incriminating evidence the investigation yields, the less comfortable Solomon feels with his intervention; as Seberg senses she’s being watched, she teeters on the brink of nervous collapse.

A fragile screen goddess in peril, then, her arc crossed with that of a government man undergoing a change of heart: It’s the stuff of perfectly engrossing fiction, yet hardly the most exciting way to frame a life with as many political and personal pressure points as Seberg’s short, doomed one. A sparking, restless performer more dynamically cast by Andrews in his 2017 West End revival of “Cat on a Hot Tin Roof,” O’Connell does his best to make his scenes feel emotionally urgent rather than procedural, but can’t make Jack a character rather than a mere device. Meanwhile, the film’s depiction of the Black Power scene, with its own tangle of internal conflicts, is particularly thin and reductive, its stakes and players receding into the background once Seberg’s battle with the FBI takes focus.

“There’s a war against black people in America, and you just got caught in the crossfire,” Jamal tells her — accurately enough, though the script itself also loses the forest for the trees. Yet on matters closer to home — the star’s crumbling marriage to Gary, her relationship to young son Diego (Gabriel Sky), the cruelly premature birth and death of her infant daughter Nina — “Seberg” is still frustratingly gauzy and surface-level, like an informative magazine profile that never quite gets under the skin of its subject. (We practically learn more of Jack’s family life, even if the ever-welcome Margaret Qualley is wasted as his feminist Jiminy Cricket of a wife.)

That “Seberg,” for all its false notes and missed opportunities, remains pretty compulsive viewing is almost entirely down to the peculiar star magnetism of Stewart — a very different animal on screen, it so happens, from the more gamine, hungry-to-please Seberg, though she knowingly captures the brittle, dissociated quality of a private celebrity still figuring out how to exist in public. (A bouquet to costume designer Michael Wilkinson, who interprets Seberg’s — and Stewart’s — tailored glamour as a kind of exquisite protective shield: One especially dazzling, tissue-pink evening gown boasts a chest-strap of diamonds like a magazine of ammunition.)

One of those actors who’s most riveting when permitted time to think on camera, Stewart can’t always make Shrapnel and Waterhouse’s clunkiest dialogue (“It’s all connected, the same disease, the same disgusting racism!”) fly. Yet she seems to pull moments for herself from the film’s busy construction: Simple, extended shots of her staring critically at herself in a mirror, or bouncing off the walls with anguish in a darkened bathroom, feel as honest and penetrating as anything here. Who is Jean Seberg? It feels like Kristen Stewart knows; it’s the film that won’t quite tell us.

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