A decided—and unwelcome—change of pace for writer-director Florian Henckel von Donnersmarck, who won an Academy Award for Best Foreign-Language Film with his powerful period drama “The Lives of Others” in 2007. “The Tourist” aims to be a sexy caper movie set against luxurious European locations in the style of Stanley Donen’s “Charade,” but it manages only one of the three essential elements—as shot by ace cinematographer John Seale, Venice is simply gorgeous. But the stars set off no sparks together and the who’s-who plot is convoluted but silly and sadly predictable.

Angelina Jolie stars as elegant femme fatale Elise Ward, who’s being watched by aggressive Scotland Yard investigator John Acheson (Paul Bettany) in France. He’s after her paramour, the infamous Alexander Pearce, who stole a vast sum of money from Russian gangster Reginald Shaw (Steven Berkoff) and owes the British government nearly eight hundred million pounds (for what reason isn’t entirely clear, at least not to this viewer). Acheson is certain Elise will lead him to Pearce, whose physical appearance remains a mystery to the authorities.

Elise gets a message from Pearce giving her instructions on how to reach him—she’s to take a train to Venice and, on the trip, link up with any man she chooses of the same height and build as he is. The detectives tracking her will assume that the guy’s Alexander, transformed by plastic surgery, and once their attention is diverted to him, she and the real Pearce can reconnect and run off with each other and scads of cash. The fellow she happens on is Frank Tupelo (Johnny Depp), a widowed—and eccentrically flummoxed—math teacher from Wisconsin.

From this point the point sickens. Elise and Frank get close. Shaw gets word of what’s going on and comes after Elise and Frank. An elegant man (Rufus Sewell) periodically appears to pass notes to Elise about where to find Alexander. There are chases on foot across rooftops and by boat in the canals. A corrupt police official (Christian De Sica) enters the scene. Acheson’s grumpy superior Jones (Timothy Dalton) occasionally intervenes.

But though all the wrinkles make things seem complex, the issue at the heart of “The Tourist” is mighty simple: who is Alexander Pearce? And though the screenplay tries to make it hard to tell, tossing out a whole tin full of red herrings along the way, it turns out that the resolution of the puzzle—while implausible—is also pretty obvious from the start. As in “Charade,” the answer lies in uncertainty about who people really are, but in that respect the cleverness in Donen’s film is replaced here by twists that aren’t anywhere near as nifty as intended. And of course, the outcome depends on everybody acting exactly the way the manipulative mastermind behind everything foresees them doing, which in retrospect seems utterly absurd.

Still, though the picture simply isn’t as amusingly deceptive as von Donnensmarck must have hoped and Depp is a grave disappointment, bringing little of his usual individuality to his role beyond a sort of wry befuddlement, there are still those lovely visuals—not merely of the city, but of Jolie, who glides through the entire thing looking like an alabaster goddess adorned in voluptuous costumes, courtesy of Colleen Atwood. She might not evince much emotion, but she looks magnificent, and it’s not surprising that on occasion the director chooses to go into slow motion to give us more time to drink in the vision. A pity that she and Depp don’t have much chemistry; they set off no fireworks in their scenes together.

Nor does the supporting cast bring much to the party. Bettany is depressingly one-note as the London detective, and Berkoff a caricature as the Russian mobster (it doesn’t help that in his big scene he has to intone some of the worst dialogue in a script with few good lines). Dalton phones in his performance. Mention should also be made of the overblown score by James Newton Howard, which swoons romantically when not trying desperately to encourage some excitement.

The “Charade” template is a very hard nut to crack. Last summer “Knight and Day” tried it with a frenetic approach, and wound up more exhausting than charming. Now Von Donnersmarck opts for a laid-back one, and winds up with a would-be sophisticated frolic so droopy and inane that the plot holes and dull performances almost obliterate the gorgeous visuals. This “Tourist” lumbers when it should levitate and sinks when it should soar.