Despite reports to the contrary, Jean-Luc Godard did not shoot the film without a script; however, he did not have a finished script at the beginning, instead writing scenes in the morning and filming them that day. See also Pierrot le fou (1965).
According to Jean-Pierre Melville, Godard asked him for consultation during the post-production stage, because the first edit was too long for distribution. Melville suggested Godard remove all scenes that slowed down the action (his own turn as novelist Parvulesco included). Instead of excluding entire scenes, though, Godard cut little bits from here and there. This led to the "jump cut" technique this movie introduced. Melville declared the result to be excellent.
According to Raoul Coutard, some sleight of hand was involved in getting a permit to shoot on the streets of Paris. A complete script was needed to obtain the permit, so Jean-Luc Godard had an assistant type up a mock script for a film that would never be shot.
This film was released around the same time as François Truffaut's Les Quatre Cents Coups (1959) and Alain Resnais' Hiroshima mon amour (1959), thus establishing what came to be known as the French Nouvelle Vague (New Wave).
Immediately after production, Jean-Paul Belmondo was convinced that the film was so bad that it would never be released. He was very surprised by the warm reception the film received.
Jean-Luc Godard: Towards the end of the movie, the bystander (wearing sunglasses and reading the paper) who recognizes Michel and runs off presumably to tell the police.