It’s rare for a Hollywood adaptation of a foreign-language movie to improve upon the original, but “Delivery Man,” an English version of the French Canadian dramedy “Starbuck,” manages the feat despite the fact that both are the work of writer-director Ken Scott. That doesn’t mean that the picture is any less manipulative or simple-minded than its source, only that it’s easier to take.

Amazingly enough, the key is Vince Vaughn, who has over the years played obnoxious, boorish characters so often that it’s hard to imagine him otherwise. But as David Wozniak, the irresponsible but big-hearted lug who learns that the sperm he donated long ago to a fertility clinic was used to sire more than five hundred children, nearly 150 of whom are suing to have his anonymity rescinded, he adds an almost childlike sweetness to the character that Patrick Huard utterly lacked in the earlier version.

Vaughn actually makes you care about Wozniak while, against the advice of his pal Brett (a winning Chris Pratt), who also serves as his lawyer, he begins intervening in the lives of the kids he didn’t know he had, beginning with a pro basketball player but moving quickly on to more down-to-earth young people—a girl with a drug problem just dumped by her boyfriend, a lifeguard, an overweight party animal, an angry barista who wants to be an actor, all of whom he tries to help or at least bond with. To be sure, the slapstick that comes from his relationship with Viggo (Adam Chanler-Berat), the peculiar youngster who recognizes him as his biological dad, can be strained, and his virtual adoption of disabled Ryan (Sebastien Rene) gets awfully schmaltzy, but Vaughn carries it off.

Less successful is David’s courtship of girlfriend Emma (Cobie Smulders), a policewoman who happens to be pregnant with his child but considers him unpromising husband-and-father material. Their relationship is never developed satisfactorily, and seems like an obvious adjunct to the main plot. Better are the scenes with his “real” family, especially his soft-spoken father Mikolaj (Andrzej Blumenfeld), the owner of the butcher shop where he works—not very diligently—as a delivery driver. (He’s no more capable in securing jerseys for the store’s basketball team photo.)

But the best is reserved for David’s interaction with Brett, a put-upon daddy who makes all sorts of cynical observations about parenthood while looking upon the case as a godsend for his career. Pratt is dryly amusing as the exasperated father and charmingly over his head in court. As good as he is, however, he doesn’t outclass Vaughn, who shows that he can handle a role that has heart as well as bombast.

The overall production is fine, with Scott directing much more smoothly than he did in the French-language version and taking advantage of the New York locations, well shot by cinematographer Eric Edwards. Ida Ransom’s production design, Mike Newell’s art direction and Sara Parks’s set decoration are all excellent, and the background score—a mixture of pop tunes and original music by Jon Brion—is less insistent than is normally the case in such fare.

“Delivery Man” doesn’t do any better than “Starbuck” did in handling the wider context of Wozniak’s story: where are all these youngsters’ mothers and fathers? It’s as though they didn’t exist. We don’t even get to see Brett’s wife, though since he has four children, presumably she’s around somewhere.

But despite the fact that it’s sentimental nearly beyond belief, the movie proves a sweetly engaging, often very funny, heart-tugger. And it gives Vaughn the best role he’s had in years.