Originally Posted by PaulasPain
I wouldn't recommend any French dinner you could find at 6pm, so I suggest you either a) have a late multiple course lunch where you can linger well into the afternoon, or b) have a nice dinner after your opera; it shouldn't be too difficult to reserve a nice table in Paris for that time.
For example, out of curiosity, I just phoned one of my favorite resto's in the neighborhood around the Bastille opera (I assume that's where you'll be), who told me they will be open for new year's eve and will accept reservations for 11:15pm. They will have a special menu, but the cuisine will surely be southwest French (think canard, foie gras, truffles, etc.), and the prices are reasonable. The place is Baracane: 38 r Tournelles (4th): +33 1 42 71 43 33. Feel free to PM me if I can lend a hand.
I agree with PaulasPain's strategy. You can even have a snack at a cafe near the Bastille Opera (like an omlette or croque monsieur) before attending the opera, and then eat like a king after the show (11 pm reservations are not difficult to make). The cab situation will be tricky though. Getting a cab that late at night is always difficult in Paris ... perhaps it would be easier to cab back to your neighborhood after the show and dine there. Then you can just walk back to your accomodations. Feel free to email me with any additional questions.