I agree with just taking an evening stroll along the river. Or, take one of the little open-top barges on the river, then stroll back to where you are staying (if that works). When we were in Paris, our hotel gave us free barge tickets for showing the Rick Steves' guidebook, so check that out, too. It's fun to see the various buildings, bridges, Eiffel, etc. all lighted up at night after touring during the day.
If this is your first major vacation (and I'd guess your first overseas flight together), set realistic expectations for each other and also allow yourself plenty of rest time. Expect to arrive totally exhausted and going on fumes (so to speak). If one or both of you are able to sleep on the flight, that's great and will help a great deal. But, you bodies will be out of whack from the time zone changes.
I always tell young couples to travel together (preferably an overseas trip) before making a lifetime commitment, because the exhaustion and stress of overseas travel will often bring out the worst in people (so you can see that in each other, if one or the other (or both of you) becomes a bit cranky and tired. I hope all your flights go smoothly and I hope you find your overnight place just wonderful, hope you have no language barriers......BUT, expect some issues will arise, and you can both see how the other handles them. Note: Just about everyone gets tired to some degree or a little cranky about something to some degree, so be ready to forgive reasonable crankiness/exhaustion. Allow some down time.
Paris is so very beautiful.
To save money, have a larger lunch and a smaller dinner. Ask the local young people where they would suggest eating, etc.
