I've spent Christmas week in Paris annually for the past decade or so (2020 being the notable exception). I usually stay in the Opera area and have always found something to eat and do. There are a handful of museums open - I've gone to the Musée Jacquemart-André and the Pompidou on Christmas Day - as well as movie theaters.

One year, I went to see West Side Story with French subtitles at the nearby Pathé Opéra theater (look for movies indicated VO or VOST which means version originale, original language with subtitles) followed by some very good Chinese food, which is the same thing I've done on Christmas at home in NYC for most of my life, except doing it in Paris was more fun.