I have always maintained that winter was my favorite season in Paris, much to the horror of Parisians, who easily get a chill. But not only is Paris more void of people in winter but also, it is possible to walk along the beautiful architecture without the leaves of the trees being in the way of appreciating the scene. Not that I do not like the trees in Paris, it is lovely for the city to be so green, but when you walk along looking up, you often miss the details of the buildings for trees.
And should you get snow that stays on the ground, then head straight for the Eiffel Tower. That might sound like unnecessary advice but trust me. Once it snows properly, all the metros and buses go on reduced service, and no one heads out. I had the entire Champ de Mars to myself, with four other people, managing to take wonderful pictures of a snowy Eiffel Tower without people. Just imagine.
Pro Tip: Every winter there are lots of ice rinks popping up in Paris, and whether you join in or not, try and go to the Grand Palais. The setting is wonderful, and it serves warm drinks as well as chilled champagne, and you can just watch others fall over.