The Bourne Identity (1988)
From The Internet Movie Plane Database
Richard Chamberlain (Jason Bourne)
Jaclyn Smith (Dr. Marie St. Jacques)
Anthony Quayle (Gen. François Villiers)
Donald Moffat (David Abbott)
Yorgo Voyagis (Carlos)
Peter Vaughan (Fritz Koenig)
After being shot in the head and falling off of a ship during a raging storm, an unnamed man washes ashore in Port Noir, France. He survives and is tended back to health by a kind English doctor. As he struggles to regain his memories, the man, Jason Bourne, discovers he apparently has some connection to an assassin named Carlos and an organization named Treadstone.
Bourne flies from Paris to New York in this.