Genies, at least in pop culture, have long been comic foils. Way back in 1940, in “The Thief of Bagdad,” Rex Ingram played Djinn, the movie’s larger-than-life genie — 100 feet tall in his ponytail and red diaper ­— as a sly, laughing soul man of lighthearted effrontery. The surrealist ’60s sitcom “I Dream of Jeannie” featured Barbara Eden, in diaphanous harem silks, as a magical servant/housewife, blinking her eyes to teleport her clueless “master” out of trouble. And Robin Williams’ vocal performance as the Genie in “Aladdin” may have come closer than any of his other film performances to channeling Williams the free-associational joke geyser.

So in “Genie,” when Melissa McCarthy pops out of a jewel box and reveals herself to be an ancient granter of wishes named Flora, it’s hardly a surprise that 1) the character is a complete lark, and 2) the whole joke is that Flora, though she hasn’t been let out of her box for 2,000 years, is nothing more or less than the latest incarnation of Melissa McCarthy’s quizzical air-popped hostility. (Presented with a slice of pizza, she says, “This is just a triangle of…red bread!”)

“Genie” was written by Richard Curtis (it’s a remake of his 1991 British television film “Bernard and the Genie”), but the movie, while set in New York at Christmastime, is no “Love Actually.” It’s more like “Elf” crossed with “Love Sort Of.” When Flora, whose full name is Flora Gwendolyn Lockheed Firepit McCallister, says those magic words “Your wish is my command,” she’s speaking to Bernard (Paapa Essiedu), who accidentally summoned her out of that box. He’s a transplanted Brit who works at a tony Manhattan art auction house — or did, until he was fired, only to come home having missed his daughter’s eighth birthday celebration. That’s the last straw for his wife, Julie (Denée Benton), who announces that she’s going to be taking some time away from him.

What did Bernard do to deserve this? The way the ingenuous British actor Paapa Essiedu plays him, he’s a painfully sweet and caring man, tying himself in knots to please everyone. Bernard worked endless hours at the auction house because that’s what his evil imp of a boss (Alan Cumming) demanded. But in the new calculus of movie comedy (seen, as well, in the current Christmas movie “Dashing Through the Snow”), there’s no excuse for being away from your family. If it looks even a little bit like workaholism, daddy is going to be in trouble.

Flora, with her wish-granting acumen, would seem to be just what the marriage doctor ordered. At first, when she pops up in her Renaissance-fair outfit, complete with blue booties, Bernard thinks she’s an intruder; he flippantly tries to prove that she’s not a genie by wishing for his phone to be fully charged and for a camel to pop up in his living room. When both things happen, we think, “Oh, no! He’s used up two of his three wishes.”

But in “Genie,” it turns out that the three-wishes thing doesn’t apply. Bernard, having unleashed the force that is Flora, can have limitless wishes. There are still rules, though. He can’t go back in time, and he can’t change people’s feelings. He’s got to use the wishes to create a situation that will win his family back.

The way all this plays out is lighter than balsa wood. Richard Curtis made his name investing romantic comedy with a surprise spark of humanity (“Four Weddings and a Funeral,” “Notting Hill”), but “Genie” really is a glorified sitcom — or, more to the point, a genie-out-of-water comedy. Flora, who is so old she was pals with Jesus Christ, is wide-eyed at the wonders of the modern metropolis. She and Bernard go to the movies (Flora to Tom Cruise onscreen: “This mission is impossible! It’s in the title!”) and they have a shopping spree at Bloomingdale’s. She washes her hair in the toilet (“Refreshing!”), dances to hip-hop (kind of cringe), and, in a pretty decent joke, thinks that someone using a weight machine at Crunch Fitness is on a medieval rack (“I had just hoped that by now this kind of torture had stopped”).

But all this high-concept hi-larity has an innocuously familiar, haven’t-we-been-watching-this-since-the-’80s? quality. (“Elf,” the comedy it all most directly resembles, came out 20 years ago.) The funny moments in “Genie,” and there are a handful of them, emerge mostly from McCarthy just tossing off lines with her dislocating insouciance. Talking about Bernard’s boss, she says, with casual sincerity, “Do you want me to kill him? I’m kind of a sword-and-slice gal.” By the time she and Bernard have become a team, she’s saying things like “This is classic Flora and Nardo stuff. Takin’ names and kickin’ butts. This is what we do!” This is what Melissa McCarthy does, and if you’re a fan (as I always have been), there’s a way it doesn’t get old.

Yet it still needs a better pedestal than “Genie,” a movie that becomes bogged down in a plot about the Mona Lisa until it finally, in a singularly cheesy sequence, jumps the magic carpet. Robin Williams was a genius, but not every movie he made was “Aladdin” or “Mrs. Doubtfire.” Melissa McCarthy needs her own “Mrs. Doubtfire” — either that, or another gripping serious role like the kind she had in “Can You Ever Forgive Me?” She’s the quipster caffeine of “Genie,” but over the years she has perked up too many second-rate, throwaway comedies, and this, I’m afraid, is one more of them. It’s certainly a wholesome Christmas cookie of a movie, so if that’s your thing by all means make it a holiday streaming snack. But it’s my wish that Melissa McCarthy would finally get the great comedy she deserves.