If nothing else, "Breathless" is a gorgeous cinematic documentation of Paris and Parisians in 1960, because the film was shot entirely on location as Godard took us to the wide boulevards and narrow streets of the City of Light and inside its gleaming commercial buildings and crammed apartments. Young Jean-Paul Belmondo with his smooth hairless chest and Jean Seberg with her tomboy-pretty face are such a photogenic couple to watch against a backdrop of vintage (at the time modern) cars and men in suits and women wearing white gloves that you'd think Godard was commissioned to make this movie to boost Paris tourism. Godard used music extensively -- jazz, big-band, classical music, and the characters in the movie are always reading newspapers, magazines and talking about books and movies. If you're amused by the expression: "Good heavens, he's so French," well, that expression fits Godard perfectly.
"Breathless" has a simple plot -- a fearless car thief (Belmondo) kills a cop and spends the entire movie trying to avoid being captured; meanwhile his object of desire, an American journalist (Seberg), tries to figure out how the hell she got involved with this charming criminal. Godard did a lot of long one-take shots, and the resulting "real-time" emotions and drama are utterly precious.
In later years, Godard got more and more experimental. I remember sitting in a theater in the 80s watching "Hail Mary", which is his retelling of the story of Virgin Mary, and was at once moved and frustrated by his relentless spirit to experiment. But that's Godard; he doesn't play by the rules, and we thank god for that.