Elizabeth Banks in “Call Jane.” Wilson Web/Roadside Attractions

Topicality is baked into the film “Call Jane,” director Phyllis Nagy’s historical drama about a pre-Roe v. Wade network of underground abortion providers in late-1960s Chicago. But for this undercooked endeavor, such relevance is more of a burden than a boon.

The real-life inspiration for this fictionalized tale – the Jane Collective, a women-run network that provided 11,000 abortions when the procedure was mostly illegal – is a genuine source of female empowerment. Still, Nagy only occasionally imbues the proceedings with urgency befitting the life-or-death stakes. Best known as the screenwriter behind 2015’s “Carol,” a master class in romantic longing and slow-burn storytelling, the filmmaker (working from a slapdash screenplay by Hayley Schore and Roshan Sethi) strains to shepherd a narrative that zips along in a haze of underserved storylines.

That can’t be blamed on star Elizabeth Banks, who portrays a housewife named Joy with a criminal-litigator husband (Chris Messina), a pubescent daughter (Grace Edwards) and a life-threatening pregnancy. After seeing her appeal for a “therapeutic termination” rejected by the hospital – a pointedly blunt scene, in which the members of the all-male panel discuss the woman before them as if she’s invisible – an incredulous Joy turns to the Jane Collective for a covert procedure.

That experience sparks a feminist awakening in Joy, who soon gets roped into joining the “Janes” as a volunteer. Banks sells the transformation from tightly wound housewife to secret women’s rights advocate, though the actress is at her best when Joy is amusingly squirming in discomfort during her early days with the Janes – even if the script promptly sweeps that initial consternation under the rug.

Elizabeth Banks, left, and Sigourney Weaver in “Call Jane.” MUST CREDIT: Wilson Web/Roadside Attractions Wilson Web/Roadside Attractions

Sigourney Weaver plays the collective’s tough-love founder with palpable pluck and world-weariness. Wunmi Mosaku does a lot with a little with her character, an impassioned activist pushing for the group to better serve Black women. Cory Michael Smith is sufficiently sleazy as the Jane Collective doctor who is only in it for the money – and may not, in fact, be a physician at all. (His coldly methodical oversight of Joy’s abortion makes for a striking, if difficult, scene.) But Messina can’t quite get a grip on the patriarchy-pushing Will, whose marital devotion cracks when Joy becomes too busy with her clandestine activism to put dinner on the table. And Kate Mara is woefully underused as the pill-popping widow next door who cozies up to Will amid Joy’s increasingly frequent absences.

Although the deception predictably comes to a head, as Joy’s husband and daughter act on their suspicions that something is awry, “Call Jane” tidies that mess with baffling brevity. The same goes for the conflict over the Jane Collective’s approach to race, which is broached and resolved so swiftly that the entire subplot reads like a last-minute rewrite. A debate in which the Janes futilely attempt to assign a limited number of free abortions – tragically weighing patients’ hardships against one another – only scratches the surface of that deeper dilemma.

The result is a film that’s engaging enough, but choppily paced and oddly inert. Beyond an audacious opening shot and some period-appropriate needle drops – Nancy Sinatra, Malvina Reynolds and Vanity Fare among them – “Call Jane” is also decidedly unstylish. After the movie premiered at the Sundance Film Festival in January, several months before the Supreme Court overturned 1973’s Roe v. Wade, the parallels between the Jane Collective’s battle to protect women’s rights and current activists’ newfound fight to restore them are even starker now – making it all the more disheartening that “Call Jane” doesn’t quite ring true.