Shia LaBeouf — an embattled veteran of blockbusters and indies — teams up with newcomer Zack Gottsagen in “The Peanut Butter Falcon,” a sweetly comic drama about a young man with Down syndrome who dreams of becoming a professional wrestler.

The story opens on Gottsagen’s character, Zak, a 20-something who has no family and, thus, has been warehoused in a retirement home. His sole link to the outside world is a stack of dusty VHS tapes celebrating the exploits of a wrestler known as the Salt-Water Redneck (Thomas Haden Church), whom Zak watches religiously.

When he comes across an ad for his hero’s wrestling camp, a little encouragement from Zak’s roommate (Bruce Dern) — and a bit of soapy lather — facilitate the young man’s escape through the bars in his window.

As chance would have it, Zak stows away on a boat stolen by a man who is also on the lam: LaBeouf’s Tyler, who, after a run of hard times, has been reduced to stealing the catches of other crab fishermen. Tyler’s once boyish, bashful spirit has long since crusted over, but Zak’s boisterous, magnetic personality softens him up.

Eventually, Tyler agrees to accompany Zak on his quest to locate the wrestling camp. He takes on the role of coaching Zak, even helping Zak devise his wrestling moniker: the Peanut Butter Falcon.

Sound familiar? The screenplay (by co-writer-directors Tyler Nilson and Michael Schwartz) essentially lifts its story beats directly from “The Adventures of Huckleberry Finn,” transposing Mark Twain’s antebellum tale into a contemporary context. During the second act, the pair even travel on a makeshift raft. By the movie’s halfway point, the source material is made even more explicit.

Set in the rural Deep South, the film features a soundtrack of country and indie rock, providing a sonic backdrop of banjo twang to the vistas of bayous and woodlands. Nilson, a native Southerner, knows the terrain well, and Schwartz, whose background is primarily in documentaries, is adept at capturing it.

Both Tyler and Zak are outlaws, each one fleeing a different form of authority that is seen as a brutally indifferent form of incarceration. For Tyler, it’s law enforcement (and the goons he stole from); for Zak, it’s an impersonal system of care facilities referred to in the film — somewhat lazily — as the “state.”

Although the men’s deepening bond is meant to be transgressive, its implications pale in comparison to those of Twain’s parallel characters: Huck, a white teenager, and Jim, an older runaway black slave. But the film’s allusions to Twain ultimately contribute to a sense of derivation, undermining the originality of the material and preventing “Falcon” from graduating from good to great.

Is its story of individual freedom vs. societal constraint heartwarming? Yes. It’s also about family: Zak, without friends or kin, and Tyler, who is haunted by the premature death of his older brother, gradually come to see that they need each other. They invent a secret handshake, split a jug of brown liquor and wrestle while wearing helmets carved from watermelon rinds.

As they travel the river sitting shoulder to shoulder, a handful of breathtaking shots chart their literal and metaphorical voyage together. Gottsagen’s performance stands out, in a solid cast that includes Dakota Johnson as a volunteer from Zak’s care facility who sets out to bring him back but ends up being caught up by the developing family affair. Gottsagen, who has Down syndrome, provides an energy that proves infectious, even when the story drags.

As for how the whole thing ends: Have you read Twain’s book? If so, you can pretty much guess where this journey down the lazy river will go.