Also keep in mind that Paris will not only be cold, but the days will be short (daylight ~ 8:30-4:30-ish), limiting your day trips. This would be a great week to stay pretty much in Paris with its great museums uncrowded (the ones open during the holidays!), and enjoying the cafes.
Versailles could be easily done, perhaps the champagne area of Reims; other that that, I'd spend the time exploring Paris.