Final answer:
The Jean-Luc Godard film that left a significant impact on young American filmmakers was 'Breathless' (1960).
Step-by-step explanation:
The Jean-Luc Godard film that impressed young American filmmakers was Breathless (À bout de souffle, 1960). This film is renowned for its innovative use of jump cuts and handheld camera work, which marked a departure from the traditional Hollywood style of filmmaking. Godard was a leading figure in the French New Wave (Nouvelle Vague), a movement embracing experimentation and personal expression in cinema, which influenced filmmakers across the world, including the United States. The novel techniques and storytelling adopted by Godard inspired a generation of American directors to explore more artistic experimentation in their work.