I don't think I'm as informed on neo-realism and the French New Wave as John or wpqx, so my view is more limited.
If we take Breathless, the way it was made would be it, as the film borrows more from american films from the 50s and film noir, imo. Neo-realism is (for me?) more about working-class people and their daily struggles. That's why some people have a problem with Ossessione being a neo-realist film, as it's also a crime-drama (based on Cain's novel "The Postman always rings twice"). But the people in it, are working-class, soo...