I had a lovely dinner on Christmas eve a couple of years ago at a restaurant on the Left Bank recommended by the PHV concierge. I have not had trouble getting a taxi on Christmas Day, but it's probably prudent to have them book one in advance. I would think you could ask them about public transportation on Christmas--my recollection is that it doesn't shut down (a la London), but runs on a reduced holiday schedule. Most things do shut on Christmas (we've gone to movies the couple of times we were there), but you will be leaving for the airport anyway.
I'd stay in town, walk around and then have a lovely dinner or, if you like ballet, go see the Onegin at Garnier and then enjoy the breakfast buffet on Christmas morning, rather than stay at CDG.