The most famous flea market in Paris is Les Puces de Saint-Ouen, known as Les Puces (The Fleas in French).
It is considered one of the biggest antique markets in the world, attracting approx 120,000 visitors a weekend!
The market is opened Saturday and Sunday till 6pm and even on Mondays till 5pm!
To get there, get the metro line 4 and get off at Porte de Clignancourt. (The 18th arrondissement). I can guarantee that everyone will know where it is.
There is an enormous selection of furniture, prints, paintings, mirrors, antique luggage, vintage clothing, hardware, art deco furniture and hardware, kitchen goods, etc etc.
As this is a busy and crowded place, highly recommended to keep your wallets tight.