I never feel there is a “best” because there were so many different films made during the New Wave in such a short period of time, that I believe it is better to give a sampling of what could be considered the best.
First, there is Agnès Varda‘s classic, Cleo from 5 to 7 (1962). This film follows Cleo (Corrine Marchand) around Paris for 2 hours in real time as she waits to hear the results from a medical test. While on the surface this might seem like a depressing film to watch, it is just the opposite – full of life, music, and drama that only an actress can bring to her own life. She even meets a solider who is leaving for Algeria the next day. It also makes you never want to get your Tarot cards read. What makes this film new wave? It was shot in the streets, on real locations, etc. It has a cinema verite feel to it. One other thing you will find cropping up in some of the French New Wave films is the topic of Algeria (and if not Algeria, Indochina) as that war was so important to France’s identity at that period in time and influenced many of the New Wave filmmakers. Also Varda was the only woman director who was part of the French New Wave. She was married to director Jacques Demy.
Louis Malle‘s Elevator to the Gallows (1958) might secretly be my favorite and it isn’t nearly as well known as the Truffaut and Godard films out there. It follows two love stories that are intertwined: that of Florence (Jeanne Moreau) and Julien (Maurice Ronet), the adult couple having an illicit affair, and Véronique (Yori Bertin), a girl who works in a flower shop and has a crush on Julien but is dating a young hoodlum, Louis (Georges Poujouly). Complications ensue when Louis impersonates Julien (a war hero who fought in Indochina) to impress Véronique and inadvertently kills a rich German couple. In the meantime, Julien is actually murdering Florence’s husband so they can be together. It is a twisted and dark tale of murder, betrayal and my favorite, l’amour fou. Like with other New Wave films, it is shot on the streets of Paris and in real locations. American cars figure into the mise-en-scene heavily as owning a large American car was a mark of status. Finally, Louis Malle managed to get Miles Davis to record the score of the film in one evening when he discovered Davis was in Paris. The soundtrack is available, at least on CD. French New Wave directors loved American Jazz and it usually features prominently in many of the films.
Jean-Luc Godard‘s Band of Outsiders (1964). This is a very late example of a French New Wave film. And I would argue that Breathless (1960) by Godard is a better example overall of the French New Wave in its heyday, but I prefer this film. Odile (Anna Karina and for a time, Godard’s wife) must choose between two best friends, Franz (Sami Frey) and Arthur (Claude Brasseur), and while the l’amour fou isn’t quite as crazy and irrational as it might be in Breathless, there is still crime, jazz, real locations, philosophical musings that only Godard can do and even a happy ending (which usually doesn’t happen in New Wave films). Hence, why this film is a good example of the end of the New Wave.
Technically, the French New Wave lasted from 1958-1964 but you can find some New Wave films through the end of the 1960s. Therefore, I cannot leave out my favorite French heart-throb from the 1950s and 1960s, Alain Delon, starring in Le Samourai (1967), directed by Jean-Pierre Melville, an extremely important French postwar director. This is a color film and features Delon as a hit-man for hire whose life seems doomed from the start. What is important about this film is that it characterizes what at least some French New Wave films incorporate into their narratives: the doomed fatalistic characters you find in earlier French Film Noirs.