Sites are open, but not all shops. Some grocery stores will open for a few hours on a Sunday morning; many shops in the tourist areas and Champs-Elysées etc are often open, as are some market areas. Do not expect the large department stores to be open except for some Sundays leading up to the Christmas season. Museums and galleries are open and busy; there is a charge for most except on certain days.
Don't go expecting it to be a regular shopping day however.
Also know that some transit lines will have a reduced schedule.