The movie ends with Bourne finding Marie in a shop/restaurant selling on a Greek island. The shop rents scooters and has a restaurant. This scene ends with Jason and Marie hugging and pulls out to show the island. It rolls right into the ending credits and song.
Remember, this is one of the few spy movies without a pre-title sequence since From Russia With Love introduced the concept of a pre-title sequence in spy movies.
As a nice touch, the red bag that Bourne got at the bank and had carried the money is hanging behind the cash register and is being used as a planter with some flowers.