Breathless by Jean-Luc Godard is an interesting film. This film was very influential, many other directors have mimicked it. (Quintin Tarrantino was a big fan.) Godard was very much influenced by Humphrey Bogart, and you can see many references to Humprhey and his films.
This film was very influential in part because of jump shots or jump cuts, in which there is a lapse in continuity. Also, Godard violated the 180 degree rule. This film alludes to the crime/gangster drama.
The characters in this film, especially Michel are influenced by the films that they see. In one scene we see where Michel sees a poster of Humprhey Bogart, and he mimics what Humprhey does. he runs his fingers around his lips, and he chain smokes as does Humphrey Bogart in many of his films.
This film talks about love in a very abstract way. You often question why the characters are doing the things that they do. Why does Michel lie about everything? Why does Patricia believe him? (who has a different car every time you see them?) We are able to see the impact that media has had on every day life. Patricia sells the paper, and again the above reference to the movies. Also, you see people buying papers all the time, Michel always does to stay current on his warrant for arrest. We see signs lit up above buildings with breaking news.
This film strongly reminded my of The Maltese Falcon by John Huston. That too was a crime film, but the strongest similarity to me was that a loved one was turned in to the police by a lover. In The Maltese Falcon, Sam turns in Brigid even though he is in love with her. In Breathless Patricia turns in Michel, her reasoning is that she needed to see if she did actually love him, and her answer was that no she did not, if she was able to turn him in. However, after she calls the inspector she seems to feel some remorse, as she tells him and tries to convince him to flee from the cops.
This film, I imagine would have been very exciting in it's day. With it's playing with the crime genre, the use of media and movie influence on the characters lives, this would have been a new idea and probably could have made a viewer quite breathless!