Museums in Paris are generally open from 10 a.m. to 6 p.m. but most of them offer later closing hours until 9 p.m. or 10 p.m. Museums do not work on Mondays and Tuesdays. However, some monuments are open 365 days a year and the main ones could be visited until midnight.
Note that admission is free first Sunday of each month.
Department stores are usually open from 9.30 a.m. to 8 pm, and until 9.30 pm on Thursday. Shops are open from 9.30 am to 7 pm, sometimes closed at lunchtime.
Shops and department stores are closed on Sundays except for certain areas (Le Marais, Beaubourg ...). Note that some shops are closed on Mondays.
Post offices are open from 8 a.m. to 8 p.m. from Monday to Friday and until 12 p.m. on Saturday.
The Post Office of the Louvre (52 rue du Louvre, 75001 Paris) is open 24/7.