The 1983 film starring Richard Gere as a car thief driving toward Los Angeles is Breathless. Gere plays Jesse Lujack, a reckless Las Vegas drifter who steals a Porsche and sets off to find Monica Poiccard, a French architecture student.
Directed by Jim McBride, Breathless is an American adaptation of Jean-Luc Godard’s influential 1960 French film À bout de souffle, also released in English as Breathless. The remake updates the setting and style for early-1980s America while keeping the central fugitive-romance story.
Jesse’s trip becomes far more dangerous after he discovers a handgun in the stolen car and fatally shoots a pursuing highway patrolman. He hides in Los Angeles with Monica, played by Valérie Kaprisky, while newspapers and police close in around him.
The title can cause confusion because the 1960 French original has the same English title. The question points specifically to the 1983 American version, which stars Gere and was released by Orion Pictures.