I agree with Louise.
Picnicking under the Eiffel Tower (on a warm evening in late August) will go down as one of my favourite memories – it seemed to be where all the locals our age were, in large groups, drinking wine, watching the tower light up every few minutes.
It was nice to eat cheaply, in a relaxed environment, and on our own time. We finished the evening by cycling down the the left bank of the river.
Here’s a picture: http://www.flickr.com/photos/caroline_1985/3191498269/