I keep hearing that there are no organized fireworks in Paris this New Year's Eve but haven't seen anything reliably definitive either way. If you go to any of the popular spots outdoors, be prepared for crowds and watch out for pickpockets and people throwing bottles and fireworks (and sometimes throwing fireworks in bottles). The metro will be jam-packed all evening and taxis may be scarce.
You're right, most things will be closed January 1, though I think there are a few other museums that will be open. Touristy areas will no doubt have a bit more activity than more residential areas.