A British woman, Elise Clifton-Ward (Angelina Jolie), is being followed by French Police who are working with Scotland Yard under the direction of Inspector John Acheson (Paul Bettany). Acheson has spent years hunting Alexander Pearce, a lover of Elise, who owes  744 million in back taxes, and is believed to have received plastic surgery to alter his appearance. At a Parisian cafe, Elise receives written instructions from Pearce: Board the train to Venice; pick out a man; let the police believe that he is Pearce. Elise burns the note, evades the police and boards the train.
On the train, Elise selects Frank Tupelo (Johnny Depp), who is apparently an American mathematics teacher from a community college in Wisconsin. She spends much time with him, seeming to start a romance. Meanwhile, the police have managed to salvage the ashes of her burned note and assembled them to extract information regarding her rendezvous, as well as her ruse. Aware of her location, but not of the ruse, an informer from the police station communicates to Reginald Shaw (Steven Berkoff), the mobster from whom Pearce stole $2.3 billion, that Pearce is traveling with Elise on the train to Venice. Shaw immediately proceeds to Venice.
Elise invites Frank to stay with her at her suite in the Hotel Danieli in Venice. Pearce leaves further instructions for Elise to attend a ball. Elise abandons Frank, who is then chased by Shaw's men. While trying to escape from them, Frank is detained by the Italian police, ostensibly for his own safety, only to have a corrupt inspector turn him over to Shaw's men in exchange for the bounty that has been placed on Pearce's head. Elise rescues Frank just before he is handed over, leading Shaw's men on an extended boat chase and finally escaping. She leaves Frank at the airport with his passport and money, urging him to go home for his own safety.
Elise is revealed to be an undercover Scotland Yard agent who was under suspension for her suspected sympathies with Pearce. She agrees to participate in a sting operation. At the ball, as Elise tries to spot Pearce in the crowd, an envelope is placed on the table in front of her, but the man (Rufus Sewell) disappears into the crowd. She tries to follow him through the crowd, but is stopped by Frank. Frank claims to be in love with Elise and invites her to dance with him. After the police surprise Frank, Elise reads the note. She leaves suddenly in her boat to be tailed by Shaw. Both parties are followed by the police. Frank is held handcuffed.
When Elise arrives at the destination, Shaw takes her prisoner, threatening to harm her unless she reveals the location of the stolen money. The police monitor the situation inside the rendezvous room through audio and video links. Despite Elise's peril, Acheson repeatedly turns down police requests to intervene with their snipers. While the police are occupied in monitoring the situation, Frank escapes from the police boat and confronts Shaw, claiming to be Pearce and offering to open the safe if Elise is allowed to leave safely. Shaw is skeptical and makes a counter offer that Frank should open the safe if he does not want to see Elise tortured by his men. Chief Inspector Jones (Timothy Dalton) arrives at the police stake-out, overrides Acheson, and orders the snipers to fire, killing Shaw and his men. To Elise's obvious pleasure, Jones lifts her suspension and terminates her employment.
Acheson, receiving a message that Pearce has been found near their position, rushes to find the police have detained an Englishman. The man, Lawrence Mason, says he is a tourist following written instructions received via his mobile phone, for which he has been receiving payments. Elise tells Frank that she loves him, but she also loves Pearce. Frank then suggests a "solution" to this dilemma; to Elise's surprise, he opens the safe by entering the correct code, thus revealing that he is really Alexander Pearce. When the police open the safe they find only one cheque: It is for  744 million. Acheson prepares to chase after Pearce, but Jones overrides him, reasoning that with the taxes now paid in full, Pearce's only crime is that he stole money from a now-dead gangster. Jones orders the case to be closed, much to Acheson's frustration. Frank (Alexander) and Elise sail away together.
Output: Why don't the Police chase Pearce after he escapes?