In this, arguably sensitive situation, I would consider a Chinese restaurant: Diep, rue de Ponthieu (not the one on rue Pierre Charron). It is tasty and with nice service, it has a very nice peking duck menu for two (in particular, they make the skin pancakes for you at your table), and has a nice, romantic setting.
Don't tell anyone, but this place worked each time for me (yes darling, that is why I haven't been in a long time).
My vote would be for:
Le Petit Troquet
28, Rue de l'Exposition
75007 Paris, France
01 47 05 80 39
This tiny, charming, little piece of old Paris (near the Eiffel Tower in the 7th),
is where I sent my parents last week to celebrate their 55th wedding anniversary.
Madame is front of the house, Monsieur is the chef and their 20-something daughter
is in charge of the breads and desserts.
Be sure to make a reservation, as there are only about 8-10 tables.
I'l second Le P'tit Troquet. Lots of antique copper pots and old Parisian ephemera decorate this tiny and incredibly romantic little restaurant. Madame Vessiere is incredibly nice, and the food is very good, the prices won't break you. She speaks English, so you can call for reservations. My wife and I eat there once every time we go to Paris. And since this restaurant is just around the corner from the Eiffel Tower, a walk before or after dinner will be equally enchanting...
Nothing against Le P'tit Troquet, but since the bistrot is so small, the whole place will become aware of your special occasion. Now if you want that...
Personally, I think a really nice, cozy and classy hotel bar would do the trick as well, especially if you order two glasses of champagne.
And sure, a nice, romantic place in the fresh air, too! What about near the twinkling Eiffel Tower (on the hour for a couple of minutes as soon as it is dark enough).