The well-known restaurants will be fully booked, so reservations should be made early. The larger restaurants host special dinners at premium prices with paper hats and silliness included on New Year's eve. You'll find them advertised in the Paris press a few weeks in advance. The smaller, more intimate restaurants may send the staff home and shut their doors tight. Christmas eve and Christmas day are quiet in Paris.
People are at home or with their families eating, drinking and celebrating.
Metropole Paris has great descriptions of past meals and seasonal events. Now you might not imagine that a train station buffet would be worth the mention. But it is. Le Train Bleu is classified as a monument historique and even if they served hotdogs and frites , it would be worth the visit. The decor of the rooms is almost overwhelming, but the overall effect is a harmonious tribute to the distinctive style of the Belle Eopque period.