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In theory, The Tourist has a tremendous amount going for it. The director is Florian Henckel von Donnersmarck, hot off The Lives of Others, one of the best movies of the last decade. His new film stars Angelina Jolie, dressed by costume designer Coleen Atwood in clothing so exquisitely elegant it might have made Audrey Hepburn envious, and Johnny Depp, an actor witty and charming enough to lure millions into not one but three Pirates of the Caribbean movies (and counting). And Jolie and Depp are in Venice, with the sun out. Driving boats.

The pitch is enough to make you swoon, but the movie itself is curiously limp. Only Venice acquits herself properly. It's an action romance, with an opposites-attract premise, but Jolie, at a career peak for icy hauteur, is so untouchably regal that pairing her with a frumped-up Depp seems like an interspecies mistake, like having a swan mate with an affable duck. Jolie plays Elise Ward, a mysterious Englishwoman whose lover, one Alexander Pierce, stole more than $2 billion from a gangster named Reginald (Steven Berkoff) two years earlier and then disappeared. Everyone who is chasing Pierce — this includes the British government, which wants him for tax evasion — is hindered by the fact that they don't know what he looks like; wire transfers indicate he's undergone massive plastic surgery in Brazil. But over-zealous Scotland Yard investigator Acheson (Paul Bettany) is certain that Elise is the key to finding him. What man could walk away from her?

Certainly not Frank Tupelo (Depp), a widowed math teacher from Madison, Wisc. When he and Elise first meet, on a train from Paris to Venice, he'd bow and scrape if he weren't trapped behind a table. He has no clue that Elise is only following instructions from Alexander to get on the train and find someone of his height and build to serve as a red herring. The disparities between them are almost comical. Maybe it's because she's trying to maintain an English accent, never Jolie's strong suit — see the Tomb Raider movies — but the main impression she gives off is of passionless poise. She smiles at Frank's cutely flustered attempts at humor, but they are the smiles of a woman deigning to show her teeth, more tolerant than actually amused.

The point of Frank as a character is, of course, that he is a fish out of water: a humble American tourist who has stumbled into international intrigue, like Jimmy Stewart in The Man Who Knew Too Much. So he's been deliberately stripped of his glamour. (Who knew this was possible?) He's washed out, maybe just a bit pudgy and wearing a scruffy beard. Whenever the script, (adapted from the 2005 French film Anthony Zimmer) gives him the slightest chance to be funny, he is. But lamentably, that's infrequently, and his wit tends to fall flat whenever he tries it out on Elise. (It's a good thing she isn't around when he answers an Italian's morning greeting of "Buon Giorno" with "Bon Jovi.") The two don't strike sparks. "I do hope the couch will be comfortable," Elise tells Frank, just after she finishes kissing him for the first time. But it's a cold shower moment that doesn't sting, since at this point we couldn't even imagine them having a real romp.

The lack of tension isn't limited to the mega-stars either. Bettany's character gets dressed down a couple of times by his superior (Timothy Dalton) but it hardly matters. When Berkoff, who has a long career of playing bad guys (Octopussy), strangles one of his Russian henchmen in a room full of people, it's not remotely scary. Even the obligatory twist at the end is less satisfying than convenient.

I'm sure the movie suffers from the unfair expectations involved in putting two of the world's biggest movie stars into the ring together for our pleasure. But I'm going to assign most of the blame to Jolie. The poor woman is always having some absurd charge filed against her, from not caring for one daughter's hair properly to somehow warping another by allowing her to dress like a boy. But I'll see those crazy grievances and raise them a new one: she's squashed Depp's considerable mojo. We never believe her Elise would have any use for his Frank. Dressed like she's headed to a Vogue shoot, her luminous eyes perfectly made up, her otherworldly, almost cruel beauty become a distraction. It's like looking into the sun, blazing away in isolation.

• Mary Pols