How did a gang of film critics break cinema's rules with Breathless?

They did it partly by choice and partly because they could not afford to do otherwise. The New Wave was a French art film movement of the late 1950s, characterised by rejection of traditional filmmaking conventions in favour of experimentation. Many of its leading directors were critics: writers for the magazine Cahiers du cinéma, including François Truffaut and Jean-Luc Godard, became leading New Wave filmmakers. They rejected the 'Tradition of Quality' of mainstream French cinema, and in a 1954 essay Truffaut denounced the adaptation of safe literary works into unimaginative films.

When Jean-Luc Godard made Breathless (1960), he envisaged it as a documentary. Raoul Coutard shot it hand-held with next to no lighting, and instead of renting a dolly Godard often pushed him in a wheelchair. According to Coutard the film was virtually improvised on the spot. The camera was so noisy that nearly the entire film had to be dubbed afterwards.

Then came the cut that made the film famous. A jump cut breaks one continuous shot in two and removes footage so that the action jumps forward in time. Breathless used them, and they tend to draw attention to the constructed nature of the film.

How the jump cuts arose is disputed. One account says Godard was told the film was too long and, on Jean-Pierre Melville's suggestion, cut scenes from long takes. Another says Pierre Rissient reported that the jump cut style was not intended during shooting or the initial stages of editing.