As an actor, Matt Damon has always had two sides: the light and the dark, the noble and the furtive, the boyishly winning and the ominously coldhearted. Early in his career, when he was that cute kid with the shiny hair and the big grin, he played characters who had a troubled layer or two, like the hero of “Good Will Hunting” (1997), but mostly he projected a decency that was unmistakable. If this were the 1950s, he would probably have been cast forever as the boy next door.

But Damon, because he has an adventurous spirit and a heap of acting talent, figured out that it would be smart not to let himself get typecast that way. In “The Talented Mr. Ripley” (1999), he gave one of the most daring performances of his generation, bringing Patricia Highsmith’s sociopathic scoundrel Tom Ripley to life as a cautiously diabolical preppie from hell.

That role, in its way, changed the course of his career. It established something essential and fascinating about Damon: that while he seemed, on the surface, to be the sort of fellow you’d want to bring home to meet your mom, what you see when you look at him is not necessarily what you get. When it came time to play the blockbuster thriller game, Damon chose a franchise film, “The Bourne Identity” (2002), that was a direct outgrowth of the gimlet-eyed darkness he’d embraced in “The Talented Mr. Ripley.” His secret-agent hero, Jason Bourne, had no memory, no affect; he was a programmed human zombie with a glare of ice. For all his charm, it was the possibility of danger beneath the clean-cut façade that made Matt Damon a movie star.

Which is all a way of saying that when you watch Damon in “Stillwater,” where he gives a gruffly low-key and commanding star performance, you’re seeing two things at once. Damon plays Bill Baker, an unemployed oil-rig worker from Oklahoma who wears a baseball cap, a goatee and a plaid shirt tucked over a junk-food belly. Bill has traveled to Marseille, in France, to try and free his daughter, Allison (Abigail Breslin), from prison. She’s a student who is serving a 9-year sentence for murder. (She was accused and convicted of killing her roommate, who was also her girlfriend.) Is she guilty? We don’t know, but since the case directly echoes that of Amanda Knox, who was — unjustly — convicted of murder in Italy in 2009 after undergoing a kind of trial-by-world-tabloid-press, then exonerated by an Italian court in 2011, we assume, watching the film, that Allison is innocent. That means that Bill appears to be on a driven and honorable crusade.

Damon, speaking in a muffled, polite, low-in-the-throat drawl, makes him a character who wants to do the right thing — to save his daughter, and to repair his bond with her (which is torn and frayed in the extreme). That all sounds like a very straightforward movie. But the beauty of “Stillwater” is that even as it has elements of being a family crime mystery, a revenge film, and a romance, it draws those elements together into a journey that doesn’t always go where you think it’s going. What holds it together is the empathy — and mystery — at the heart of Damon’s performance.

We want to see Bill, the wayward-father-as-investigator, cut to the heart of what happened. He is, in a sense, a hard-ass knight. But he’s also a deeply suspicious, reined-in man with an ax to grind. He needs a place to stay and crashes at the apartment of Virginie (Camille Cottin), a local stage actress who has begun to help him with the investigation (it’s an infamous case, and she’s drawn to big causes). When she asks Bill if he voted for Trump, he says no — because he served time in prison and didn’t have the right to vote. The answer, in other words, is, “Yes, I would have voted for Trump.”

That, in its way, is a signature moment, because it’s liberal Hollywood, for the first time, presenting a Trump supporter in a sympathetic light. But what, exactly, does that mean? “Stillwater” doesn’t get into the nitty-gritty of politics; Damon himself, who based the character on an oil rigger he met in Oklahoma, has suggested that someone whose livelihood depends on the oil industry would likely be a classic red-state voter, and he’s right.

But in “Stillwater” that’s not the ultimate meaning of Bill’s Trump side. Damon, drawing on the ethos of Dark Matt, gives him an underlying ruthless quality, a distrust that Bill wields like a weapon; it’s a quality that lends him power, but also one that needs to melt. Bill is a contradiction: a pious, praying Christian who carries himself like a heartland Teddy bear but is fueled by a buried misanthropic resentment. He has come to France to do things “the American way,” and the movie both celebrates and questions that. It shows how Bill has to wake up to something larger than the ferocity in himself.

The more he does, the closer we feel to him. And it’s all about Damon coaxing the character’s humanity out from under a stonewall of containment. “Stillwater,” if you go with it, is a highly absorbing movie, but it’s not some slow-motion action film. As directed by Tom McCarthy (“Spotlight”), it has an open-eyed, experiential quality that feels at once European and ’70s American. It’s about how trying to exonerate his daughter (by hunting for the real killer) transforms Bill from the inside. The movie performed modestly in its opening weekend, yet it presents, for the first time, a template for the kind of serious picture that could actually unite red- and blue-state moviegoers. Hollywood films once exuded a certain karmic clout, and that promise is folded into “Stillwater”: that just maybe, somehow, we could all find a way to start rooting for the same things again. It’s Damon who brings that promise alive by making Bill Baker a torn soul out to heal himself. He’s the rare actor who plays to both sides of our divide.