I think it's a really romantic and beautiful city!
I suggest to visit Paris only by foot... We had long walking hours but in this way we could see a lot of nice streets and ancient buildings.
Here you can see a lot of artists and little stores in a really special mood
In the Latin Quarter of Paris you can eat etnic food (but also traditional) for good prices.
You have also to take a cruise on river Senna! Ask for Bateaux Mouche or Bateaux Parisienne... you can book a lunch or a very romantic dinner on the boat while visit Paris from another point of view