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No, the title isn’t an over-caffeinated typo for a documentary about baristas. Nor is “Starbuck” a biopic about the chief mate in “Moby-Dick.” Instead, it’s an earnestly feel-good comedy that takes its name from the nom de plume, so to speak, of an exceedingly diligent Quebecois sperm donor.

This is how diligent David Wozniak (Patrick Huard) has been: He donated 693 times over the course of 23 months. That’s an awful lot of what Kevin Spacey, in “American Beauty,” calls chafing the carrot. Who says Canadians are bland and predictable? More important, 533 of those donations produced offspring — and now, a couple of decades later, 142 of the children Wozniak fathered have jointly filed suit to have his identity revealed.

If that weren’t enough to contend with, David has somehow gotten himself on the hook with some loan sharks for $80,000. He works as a delivery driver for his father’s butcher shop, so coming up with the cash is a problem. Then there’s the fact that his former girlfriend (Julie LeBreton) announces that she’s pregnant with his child. Number 143, as it were.

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So far, so vaguely Adam Sandler: feckless middle-aged schlub fumbles and bumbles his way through vaguely raunchy high concept. In fairness, Huard is more appealing than Sandler, who’s nowhere near as good at amiable bewilderment. If Sandler had a taste for poutine, the English-language remake could already be in front of the cameras. “Really Happy Gilmore”? “Punch-Drunk Donation”?

Except, that is, for two things. The actual English-language version, called “The Delivery Man,” stars Vince Vaughn and comes out this fall. The other is that about a third of the way into the movie, “Starbuck” starts to go touchy-feely sentimental. As part of the lawsuit, David receives a file with the names and photographs of all those plaintiff-children of his. Or plaintive children, as the case might be. Without identifying himself, he starts tracking them down. One’s an aspiring actor. David helps him get a part. Another’s a lifeguard. David (not on purpose) gets saved by him. One’s a soccer star. One’s a junkie (!). One has such severe disabilities that he lives in an institution and can’t communicate. Now who was it exactly who filed suit on his behalf? Plausibility is not a “Starbuck” priority.

The distance for David between donor and dad gets smaller and smaller. Should he reveal who he is? Stop contesting the suit? Clear his schedule for the mother of all Father’s Days? Antoine Bertrand, who bears an unnerving resemblance to Fatty Arbuckle and serves rather the same purpose here that Jeff Garlin does on “Curb Your Enthusiasm,” plays David’s equally feckless lawyer. Bertrand does his jelly-belly best to keep “Starbuck” a comedy. But even the broadest shtick can’t prevent a movie that features a Busby Berkeley-style group hug from becoming a male weepie. Or a testimonial to Planned Parenthood.