We spent last Christmas in Paris, and yes, a lot was closed but there was plenty to see, including the Pompidou center museum:
Here are this year's hours:
Saturday 24 December: 11 a.m. to 7 p.m. (the ticket desks will close at 6 p.m.)
Monday 25 December: usual opening hours (11 a.m. to 9 p.m.)
I think the Eiffel tower is open as well.
Ask your hotel to help with reservations for a nice restaurant on Christmas Day. There are a lot of Parisians who don't cook in.
Have fun!