What are romantic places to visit in Paris?

I will be visiting Paris for two days in juin. I am looking for romantic restaurants, districts, things to do for a couple.
We have been to Paris before but have seen only the usual tourist stuff. By Sue_CJust a quiet walk along the Seine at dusk, in a gentle rain, with your lover. Doesn't get much better than that.

stay in your home town and read a book
the Eiffel tower
I liked the roof of Sacre Couer, you could see for miles from up there. We got engaged in the gardens in front of the eiffel tower, that was pretty romantic?!?
The Eiffel Tower it's beautiful at night!!
the hanging gardens of babylon.
Eiffel tower sucks when you look at it up close. I was disappointed. There are cool boat rides, little cruise ships, around the eiffel tower though so you can ride those little ships and they give you a tour of the city. I think those are pretty romantic!
visit a museumor go touring and dont forget the eifel tower its really romantic at night
... What isn't romantic in Paris?

The Bateaux Mouche(s) are rivergoing boats that go up and down the Seine. I'm not sure if you consider this a "usual tourist stuff", but at twilight or night they can be quite impressive.

There are plenty of small corner restaraunts in the Latin Quarter. I remember a divine crepery very near the miniature statue of liberty along the Seine. The sights to see nearly anywhere are breathtaking.
Anywhere in that city turns me on.