There are a range of different techniques used.
Firstly, it uses Traditional Animation and in particular, Cels. Cels can be described as follows:
The cel is an important innovation to traditional animation, as it
allows some parts of each frame to be repeated from frame to frame,
thus saving labor. A simple example would be a scene with two
characters on screen, one of which is talking and the other standing
silently. Since the latter character is not moving, it can be
displayed in this scene using only one drawing, on one cel, while
multiple drawings on multiple cels are used to animate the speaking
There is a great pictorial example on the link above. It also uses CGI for some sections of the film.
This was what the director, Sylvain Chomet had to say about the animation technique (in an interview with the BBC):
I wanted to do things in animation that hadn’t been done before. It’s
a very rigid medium in what people think it should be. It’s always got
to be for kids. It should bring good feelings, have bad guys and good
guys, and end with a moral. But this means there are lots of subjects
and things you can’t show, like someone smoking a cigarette for
example. With “Belleville”, the aim was to go against that, and do
something that wasn’t aimed at kids. It’s great that kids can enjoy
the film, but it freed us up to go in directions that the animated
movie hasn’t gone in before.
In the same interview, he also commented on why he used CGI:
It was mainly to get rid of all the boring stuff. Objects, for
example, always take a very long time to animate because they don’t
change as they move. We used CGI for the cars, the bicycles, the boats
and the trains, and it meant the animators had more time for enjoyable
elements like the character acting.