A picaresque journey from Virginia to Florida with some unlikely traveling companions, “The Peanut Butter Falcon” is a small film with a big heart. It is also notable for a casting choice that gives it special distinction, though one hopes that it’s one that will become less extraordinary in the future.

It involves Zack Gottsagen, who plays Zak, a young man with Down Syndrome who has been placed in a nursing home in Richmond because the state has no other facility in which he can be housed. Gottsagen actually has the condition.

Frustrated after spending years in the home in spite of the kindness shown him by sympathetic nurse Eleanor (Dakota Johnson), Zak engineers his escape with the help of his cantankerous roommate Carl (Bruce Dern, as usual delightfully crabby), though it leaves him clothed only in his underwear. His aim is not merely freedom, but the fulfillment of a dream to study pro wrestling at a Georgia school run by his idol Salt Water Redneck (Thomas Haden Church), a grappler whom he’s watched obsessively on old video tapes.

Meanwhile Tyler (Shia LaBeouf), a fisherman struggling to make ends meet since the death of his brother Mark (Jon Bernthal, seen only in flashback), falls afoul of his nasty rival Duncan (John Hawkes), and retaliates by releasing the guy’s catch of crabs. He then flees in his rusty old boat, with Duncan and his minion Ratboy (Yelawolf) in pursuit.

What Tyler doesn’t know is that Zak has hidden himself under a tarp on the boat. And when he does discover the young man, he’s not at all pleased. But he reluctantly takes the young man under his wing, teaching him to swim and shoot a gun along the way, and they develop a fraternal bond.. Traveling by boat, raft, and on foot, they proceed down the Virginia and Carolina coasts, but not entirely alone: Eleanor catches up with them and creates a threesome. But of course there’s always the danger that Duncan and Ratboy will show up as well.

In his chance meeting with Eleanor at a general store, Tyler mentions that the young man she’s seeking might be living his own version of a Mark Twain story like Huckleberry Finn, and that’s precisely what “Falcon” is; and while it might not match its model (what movie could?), it’s a genial modern variant. It too is episodic, making room for vignettes along the way, the best probably being an encounter with a pistol-packing blind man (Wayne DeHart), who insists on baptizing them before giving them provisions to continue their odyssey.

The essence of the tale, however, is the relationship that develops between Zak and Tyler, and as played by the open-faced, enthusiastic, utterly committed Gottsagen and LaBeouf, who morphs with considerable nuance from the surly young man of his first scenes to the caring fellow of the final act, it’s a touching one. This is the story of Tyler’s redemption as well as Zak’s engagement with the world, and LaBeouf makes it credible. Johnson’s Eleanor has less shading than her eventual companions, but the actress endows her with the necessary sweetness.

The movie culminates, of course, with the trio’s arrival at the wrestling school, which is hardly the thriving enterprise that Zak expects. But Salt Water (an engagingly crusty cameo by Church) proves as open to his would-be student’s charms as Eleanor and Tyler, and enlists others—played by Jake “The Snake” Roberts and Mick Foley, elder statesmen in the pro wrestling world—to help Zak realize his dream, though the outcome avoids the note of easy triumph one might anticipate.

Directed in a gentle, unfussy manner by first-timers Tyler Nilson and Michael Schwartz, who wrote the script with Gottsagen in mind, “Falcon” boasts a production design (by Gabrael Wilson) that captures the seediness of the surroundings without overemphasizing it, and naturalistic cinematography by Nigel Bluck, and moves at unforced but not languid pace thanks to the editing by Kevin Tent and Nathaniel Fuller. The music by Jonathan Sadoff, Zachary Dawes, Noam Pilekny and Gabe Witcher is supportive, not intrusive.

“The Peanut Butter Falcon”—the title comes from the name Zak chooses for his wrestling persona—is a lovely tale of an unusual friendship, one that earns your affection rather than demanding it.