After they leave, the police spot him again and there is a car chase.
Marie’s car is an old beat-up Mini. In the Mission: Impossible and James Bond films, they are usually driving high-end sports cars (boats or motorcycles) in their chases. Even in The Italian Job, a new shiny Mini is used for the chase.
Seeing the old Mini being chased around Paris really is a nice change of pace for this type of chase. It is a throwback to Bond driving the Citroen in For Your Eyes Only (1981). As part of the Bourne chase, they drive down a steep stairway which is a great effect. They leave her car in a parking garage and Jason tells Marie that she can never come back to the car.