What are some ways to save money on a trip to Paris?

I want to plan a trip to Paris (France) with my wife. However, it looks like it's going to be really expensive. Are there any ways to save a substantial amount of money on the flight, hotel, food, anything like that? Obviously we'll do as many free or cheap tourist attractions as we can, but the flight and the hotel are really going to kill us. Ironically, I think I found the cheapest flight not on any of the discount travel sites but on Air France's website. Thanks!