Michael Stipe of the band R.E.M. once sang, “If you believed they put a man on the moon,” part of the hit song “Man on the Moon.” With that line, the singer and lyricist was referring to conspiracy theories surrounding the history-making 1969 lunar landing. “Fly Me to the Moon,” the new movie starring Scarlett Johansson and Channing Tatum, deals directly with one of these specious speculations — the one suggesting the touchdown and moonwalk were staged.

As a comedy drama riffing on the spacey theory, the film occasionally works, with real historical events adding jet fuel to the plot. Its main failure lies with the romance between the two stars, which never achieves liftoff, leaving the picture’s emotional center grounded. When the movie does soar, it’s primarily due to Ms. Johansson, on her sheer star power alone. 

Mr. Tatum plays Cole Davis, a former Air Force pilot who flew sorties in the Korean War and is heading up the base blastoff of the Apollo 11. Ms. Johansson’s character is Kelly Jones and she’s a wily New York advertising director. The year is 1968, and after a couple of scenes establishing the two characters in their respective milieus, Kelly is visited by a Moe Berkus (Woody Harrelson). Moe works for the government in some shadowy capacity and, after mildly threatening to expose Kelly’s shady past, compels the intrepid marketing exec to take on a new client: NASA.

Soon, Kelly arrives in Florida with her assistant and before she even sees a rocket, she meets Cole in a diner. Their meet-cute is, well, cute, but it doesn’t sizzle, particularly since it’s cut short for no apparent reason of plot or character. When next they meet at Cape Canaveral, the no-nonsense Cole is immediately antagonistic upon learning she’s there to improve NASA’s image with the public. They trade cynical barbs about “the American people” and eye each other curiously/dismissively, yet the whole opposites-attract thing feels uninspired and prefab, much like the ’60s set design and clothing. 

For the next hour or so, the pair butt heads as Kelly begins to secure partnerships for NASA with brands like Omega, Rice Krispies, and Tang. This is all done to increase the popularity of the space program, which in turn pressures Congress to continue its funding. The dramatic stakes are pretty low, though, and that leaves montages, splitscreens, and the vintage soundtrack to do most of the zippy work. 

The film’s rom-com elements could have made up for this lack of narrative thrust, but the two performers are not on the same wavelength and generate very few romantic vibes. Ms. Johansson, with her period cat eye makeup and Marilyn Monroe styling, plays it broadly but brilliantly, aware of the overall tone. Mr. Tatum, unfortunately, is in a completely different movie, one that’s more serious and heroic. 

Although he has the right look, with his chiseled features and flat, Brylcreemed hair, the actor’s stiff physicality and pursed lips come off awkwardly, and not in a humorous way. Also, that director Greg Berlanti did not put a stop to his constantly placing one or both of his hands into his pants pockets signifies that both actor and director are at a loss on what to do with the character. 

Having worked primarily in television, Mr. Berlanti lays out the narrative with TV comedy beats, albeit with a larger budget. His supporting cast, including sit-com alumni Ray Romano, Jim Rash, and Mr. Harrelson, all have fun with their stereotypical roles, adding some genuine fizz to the proceedings. Occasionally, too, the screenplay by Rose Gilroy, daughter of actress Rene Russo and screenwriter Dan Gilroy, alights on a clever line, yet for the most part the interpersonal dialogue feels perfunctory and the setting details generalized and unconvincing.

During the movie’s second hour, Kelly’s mission changes; no longer does she have to remind Americans about the importance of NASA but now she must actively create an alternate moon landing should the real one go wrong. This gives “Fly Me to the Moon” an actual plot and some much-needed oomph, as she has to hide this hangar production from Cole, leading to rom-com duplicity and a countdown of sorts to a heart-to-heart scene. There are also compelling sidelines involving a televised interview with Cole and a trip to a conservative senator’s house, which further explore the film’s themes of deceit, honor, and duty.

As the story races to its climax, and the staged landing becomes the government’s preference for airing live due to fear of the mission’s failure, contrivances accumulate, not least of which is the idea that no one thinks to pre-record a segment to transmit “live” to the networks, or to have a transmission delay. 

Yet viewers won’t be watching “Fly Me to the Moon” for its technological logic or historical accuracy. They’ll come for the stars and hope for some chemistry and sparkling moments. What they’ll get is a mechanical mash-up of “Mad Men,” “Hidden Figures,” and “First Man” wired to sit-com scenarios — wholly Hollywood and almost entirely forgettable.