I second both Le Cinq in the Four Seasons and Taillevant for 2 outstanding Michelin 3 star places. However, it may be interesting to consider:
L'Astrance in the 16th; L'Atelier de Joel Robuchon; La Table de Joel Robuchon; or Hiramatsu. Doing a search on these restaurants in this forum, the Paris forum and websites mentioned by other posters should yield good information on these places generally. Specific information on New Year's Eve is likely best from your hotel concierge.
Good luck