The German director of the sublime, subtle and chilling surveillance thriller “The Lives of Others:” might not have been the best choice for tackling the dressy and daft spy romance, “The Tourist.”

But even if Florian Henckel von Donnersmarck lacked the light touch this Johnny Depp/Angelina Jolie thriller required, it’s not his fault it goes off the rails. He shows a deft hand with the movie’s babe, boats, bullets and billions formula. Then the script piles the preposterous on top of the absurd and the film’s thin charms dissipate, revealing the creaking movie star contraption underneath.

Jolie is Elise, “the Target,” a head-turning British bombshell on the lam in Paris, followed by Interpol, tracked by Scotland Yard. She reads a note that puts her on a train to Venice.

“Pick someone my height and build, and make them believe it is me,” the note reads.

That someone turns out to be Frank, a Madison, Wisconsin community college math teacher, played with as much frumpiness as Johnny Depp can muster. Elise sits opposite him and bowls Frank over.

“I’m a mysterious woman on a train,” she purrs. What could her story be?”

That cute meeting gives us clues. And the cops – Paul Bettany is the obsessed inspector tracking an elusive fugitive named Alexander Pearce – let us know that there’s a lot of stolen mob money attached to this fellow, and that he has changed his appearance.

Frank, in the best Hitchcock tradition, is just another dopey American – he repeatedly sputters in Spanish to Italian waiters, clerks and police – in over his head.

There’s a generic Bond villain (Steven Berkoff) chasing the mysterious “Pearce,” and an out-of-place Englishman (Rufus Sewell) who never seems to be far from Frank, whom Elise has lured into her hotel in Venice, sending cops and gangsters into a tizzy. Might Frank by the missing Pearce?

The first gun appears at about the 43 minute mark. The first boat chase comes shortly thereafter. It’s a formula romantic thriller – “North by Northwest” with canals. As long as you realize no harm can come to our potential lovers, you can sit back and enjoy the opulence, the conspicuous consumption and the scenery.

And I’m not just talking about Jolie, who spends much of the picture striking one alluring supermodel pose after another. Neither she nor Depp (No, he didn’t get a haircut) convince us that they’re anything other than pampered movie stars getting paid to do fake hijinx in one of the most romantic cities in the world. Think “Sex and the City” with gondolas and gunfights.

Von Donnersmarck tries his hand at slapstick chases (not bad) and comic flirtation (ditto). He is still overly fascinated by the technology of surveillance, so much so that he never gives the stars the chance to develop the chemistry that the leaps in logic in the script require.

And the stars – whatever their pay grade – don’t deliver that chemistry on their own. Depp is never convincingly addled, Jolie never emotes through the plastic pretty façade created for her and her character.

But failings aside, there are worse ways to kill 100 minutes than in the company of two beautiful people in that beautiful city, being chased by fabulous speedboats, shot at from the fabulous bridges, making out in fabulous hotel rooms.

Cast: Johnny Depp, Angelina Jolie, Paul Bettany, Timothy Dalton, Rufus Sewell

Director: Florian Henckel von Donnersmarck

Running time: 1 hour, 43 minutes

Industry rating: PG-13 for violence and brief strong language.