The most famous flea market in Paris is Les Puces de Saint-Ouen, at Porte de Clignancourt. It is the largest antique market in the world, with about 150,000 visitors each weekend. There are a lot of details about the different sections of this flea market at Paris Perfect, and a lot of photos at The Paris Apartment.
Marché aux Puces de la Porte de Vanves is my favourite – it’s smaller, cleaner and more easily accessible.
Here’s an iphone app about the Paris Flea markets.