This is a must do while you're in Paris: Go to one of the many farmers markets, cheese shops, patisseries, wine shops, etc. and have a picnic at the Champ de Mars. This is the large grassy field looking at the Eiffel Tower.
Since a lot of the restaurants around the Eiffel Tower can be pretty touristy and overpriced, Chris and I decided to do as the Parisians do and get our dinner from the market. It's so romantic to sit in the park and watch the sun go down behind the Eiffel Tower while sipping a bottle of Bordeaux and nibbling on a delicious baguette with brie.
PS there are tons of "vendors" selling wine, beer and champagne in the park all night. Just make sure you watch your belongings and you don't pay full price - we negotiated the price of champagne down to €5. We were having such a good time we bought a bottle.. or 2.. or more..