Lots of great suggestions here, but I must second the opinion of SST. The Hotel d'Angleterre is absolutely wonderful, and very French. It's actually the former British Embassy, hence the name. Rooms range from small to quite large, but the bathrooms are updated and the furnishings are quite nice. The one and only drawback is no air conditioning, so if you go in August beware the heat!
There is also a service, based in London, that provides apartments for very reasonable prices. I tend to be in Paris for less than a week at a time so I haven't used it, but I have several friends who have and they've found it to be great. Apartments range from budget to ultra-luxe, so you get a wide range of prices to choose from. Check out their website at
http://www.londonconnection.com/paris_new/index.html
Bottom line, though, is I've never had less than a fantastic time in Paris! Hope it's wonderful for you, too.