Thank you for your opinions as to traveling & to the weather . I am hoping to avoid the crowds.
In the north of France it is generally cold (hovering below 50F most days) and can be rainy/blustery. If you are in Normandy out tramping around in nature, it can be quite bracing! A couple of years ago we were in Paris in January and enjoyed a spell of below freezing weather - so that is also possible. Daylight hours are short, of course.
You will be able to avoid the sorts of hordes of tourists that are typical in summer, though, and I think the weather is worth it for that!
I've done winter in Paris and Northern France twice - I was there one year from Dec-Apr and another year from Aug-Jan. My take on it was that Paris is very similar in climate to Atlanta, where I live. In spite of northern France being on a much higher latitude, more similar to Canada, the weather in Paris didn't seem any colder to me than north Georgia (I don't know why!). That is to say that it gets cold - like in the 30s-40s Fahrenheit - but I never saw snow either winter I was there and there were no transportation issues.
I was in Picardie one of those winters (what is now known as the Hauts-de-France region) and it was about like Paris - it hovered just above freezing, but I didn't see snow. I'm guessing it was colder than Normandy since Normandy is slightly south and closer to the coast (but I can't tell you that for SURE, maybe a local can chime in on this.)
However, I did visit northeastern France in December where there was snow and ice, and it seemed a LOT colder than Paris. That's the only place I saw snow in France either of those winters.
PS...one thing to keep in mind when visiting in the winter is that it gets dark early which can really cut your day short. I was there alone as a woman on one of those trips, so felt I had to be in by dark unless I was with friends. That may or may not apply to you, but it is something to consider.
Cold, wet, windy, and dark. The thing most people don't consider is that you're going to get low clouds and fog, rain or snow at least every other day, and it's going to feel colder than the actual temperature. But you will miss the summer tourists.
If you plan to do indoor activities you'll be good. If you want those great views of the monuments, and Paris at night, or a stroll along the Seine in the evening, you'll understand why that's rarely the background in the movies.
Having lived in Normandie for several years, I can tell you that you can safely assume most days at that time of year will be cloudy, precipitation will happen often, the wind can be quite strong, and sunset will come early, usually shortly after 5 P.M. Snow is rare but happens once or twice a year during that time of year. When it does happen it can amount to 10 cm or so.
More of importance to tourists is that many restaurants, and some sights, are closed for the season, so your options of where to eat out and things to see are more limited than during the spring, summer, or fall. You're coming to the end of the mussel season at that time of year, so you may find it difficult to find local moules (mussels) in restaurants and poissoneries (seafood shops).
Large cities are fine in January, the provinces not so much. Tourist shops close from November to April, while many that serve locals close for a rest after the holidays.