A French bob is a short bob with bangs and sharp lines. As with any hairstyle giving a precise definition is never possible, but in general the bangs are cut to fall at the eyebrows, the longer hair falls somewhere between cheekbone to chin, and all hair is straight-cut. It is generally given some body, either through layering of a wave (or both), and is often intended to look slightly unkempt. Like the Cleopatra bob, it is overwhelmingly associated with dark hair, although this is not a requirement.
The French bob is also sometimes known as the Parisian bob; it was popularized by French actresses in the 1920s, and it and close variations were popular among the flappers; more shaped cuts may be called a flapper bob. A modern variant is the cowgirl bob, which is a bit shaggier and longer than a French bob.
This cut is perhaps most recognizable as Amélie's haircut from the film of the same name.