The 28-minute "La Jetee" by Chris Marker from 1962, which was remade into the nearly 2-hour 12 Monkeys in 1995. 12 Monkeys was a big jump from the source material. La Jetee was told almost entirely in still photos and narrative, without expensive sets or excessive special effects, but it is a distinctively haunting work. Here's a sample:
In 1983, Le Dernier Combat was a stark, post-apocalyptic film played out between two apartment buildings between the last remnants of humanity. It is notable for it's long use of silence. It has virtually no dialog. Again, special effects are minimal but the black and white cinematography is very effective in its modern usage.
And finally: Jean-Luc Godard's 1965 film Alphaville: A Strange Adventure of Lemmy Caution is one that is frequently watched and cited as an influence on Blade Runner. I would say that this is probably the hardest of the three to really get into. These days I would strongly recommend reading a plot summary of it before tackling it. However, it's something when you have an artificial intelligence wrestling with the poetry of Jorge Luis Borges, and I would say give it a chance, especially if you want to build an understanding of what early 20th century dystopias were expected to look like.
For an added bonus, I'd throw in Orson Welle's take on the Kafka story, The Trial. It's not French, but it fits in nicely with a weekend of stark black and white dystopias: