Alexandra Simpson’s “No Sleep Till” is a gentle film, unassuming and kind. Although it’s touted as a “hypnotic take on the disaster film,” Ms. Simpson’s picture has little in common with mainstays of the genre like “The Towering Inferno” (1974) or “The Impossible” (2012). This is no star-studded venture and Ms. Simpson’s cinematic approach is anti-epic even if the event on which “No Sleep Till” revolves is serious business. Take it from an unnamed observer in the picture as he drives through a sheet of rain caused by an oncoming hurricane: “This is scary as hell.”

Ms. Simpson’s movie is a kaleidoscopic portrait of a small community in the pathway of a natural disaster. Some of its characters are more fleshed out than others, but even the briefest of cameos is endowed with a gritty homespun poetry. Ms. Simpson, who also wrote and produced the film, namechecks the author Raymond Carver in the press notes. “No Sleep Till” is marked by a narrative concision similar to that of Carver’s, a sense that an elliptical conversation or the slightest of gestures can contain volumes.

“No Sleep Till” takes place at Atlantic Beach, a city of about 13,000 people at the northeast corner of Florida. Ms. Simpson’s camera alights on precincts that are, in economic scope, modest or hard-scrabble. Storm clouds roll in; the air is steely and dense. An evacuation is in process: Public address systems advise all citizens to vacate immediately. Tourists, already living out of their suitcases, are quick on the uptake. The locals lolligag. Young folks party; a father and his two children take selfies under ominous skies. They’ve seen this all before.

Some characters are eager to see it again. The first person we encounter is a frizzy-haired 20-something who lives out of his pick-up truck. Taylor is portrayed by Taylor Benton, a real-life storm chaser whose relentless pursuit of bad weather has earned him the nickname “Tornado Genesis.” The niceties of human contact are foreign to him — when strangers reach out with goodwill, Taylor is noncommittal and monosyllabic. He’d rather watch the Weather Channel.

The primary emphasis of Ms. Simpson’s ensemble of oddballs, misfits, and people just getting by is on Will (Jordan Coley) and Mike (Xavier Brown-Sanders). Will is at a local honky tonk attempting to entertain a crowd that is more interested in drinking beer and sinking the 8-ball than stand-up comedy. When a stranger begins razzing Mike, the two men get into a dispute about the ugly rumors surrounding a woman who turns out to be the heckler’s sister. Barflies who couldn’t have bothered to take notice do so when tension flares up on stage. And then — out goes the spotlight.

Friends of long standing, Will and Mike have done this before — performance art as guerilla theater. Mike enjoys the artifice, but he’s content with life in the sleepy burg of Atlantic Beach. Will is ambitious: He’s bristling to get out of town for the sake of his career. He’s heard promising things about the scene in Philadelphia. Why not head up north? The hurricane is doing us a favor. Mike capitulates and our duo begins their evacuation, dreaming of, if not the big time, then a bigger time.

Other characters weave in-and-out of “No Sleep Till” and additional situations transpire, sometimes linking up, sometimes not. There’s a lovelorn adolescent, a grandfather-and-granddaughter team of pool cleaners, and a middle-aged woman, recently laid off and on the road, who goes for a midnight swim. 

A Parisian in America, Ms. Simpson grew up summering in Atlantic Beach — dad hailed from Florida — and retains a feel for the city’s haunts, byways, and denizens. Does a strain of geographical remove allow for the clarity and tenderness with which our auteur navigates a culture that can seem so foreign to many of its own countrymen? Perhaps. In the meantime, Ms. Simpson has made a movie of rare and welcome intimacy.