The Sunday Shutdown
By law, Sunday is a day of rest in France. Large supermarkets are closed. Most boutiques in standard neighborhoods are closed. If you need groceries on a Sunday afternoon, you are mostly out of luck.
What Remains Open
The Marais (due to its historical Jewish heritage) remains fully open on Sundays. The Champs-Élysées (designated a tourist zone) is also open. Museums and major monuments are generally open on Sundays (many close on Monday or Tuesday instead).
The Sunday Market
Sunday morning is the traditional time for outdoor food markets (like Marché Bastille). They usually pack up sharply at 1:00 PM.