As you are from New York, I wouldn't worry too much. Someone from the Sahara or Florida might have a harder time

Yes, it'll be cold, but I don't think you notice it that much as you are constantly moving. Waiting, standing still, for a parade or fireworks is the hardest.
On average it's about 40 degrees in January. Lowest 5 degrees, highest 60 degrees Fahrenheit.
In Germany they have a saying: There is no bad weather, just inappropriate clothing.
Bring your gloves, your scarf, your beanie, extra layers. And just in case, an umbrella/poncho.
And depending on how you look at it, you can be lucky and see
Disneyland Paris covered in snow.

You can also be unlucky if you do not like snow.
Keep in mind, it can get busy that week. Children in Europe don't return to school till the 6th of January.