oneguy,
All the recommendations above are excellent for Paris. One thing my wife and I learned about eating in Paris. There are some 15,000 bistros or brasseries in Paris scattered all over the city in every neighborhood. Parisians eat out about 3 nights per week, and they go to one of their local bistros. A Bistro is roughly equivalent to a diner or a neighborhood restaurant.
I say roughly equivalent because the atmosphere is quaint and informal, the food reasonably priced, but that is where the similarity ends. The quality of the food is out of this world, because these bistros are vying for the local clientelle, and being Parisians, they have very high standards on food.
So you go to one of these bistros and order La Prix Fixe, which is their special that night. It will be a number of courses of different French country style dishes, all with fresh ingredients trucked in from the countryside that day, and cooked into something that is out of this world. The actual dishes will vary from night to night and from bistro to bistro, but it doesn't matter. It will all be the best stuff you have ever tasted.
My wife and I were there for about two weeks and except for one evening at a restaurant with white table cloths and snooty waiters, it was all bistros and all prix fixe for us. We just picked out the place from a good book called Cheap Eats in Paris, we ordered the Prix Fixe, and the house wine and have never eaten better.
Places I can recommend:
Allard
L'Ami Louis
Aux Lyonnais
Le Bistrot de Cancale
Le Bouclard
Le Comptoir du Relais
Chez Georges
L'Oenotheque
Au Petit Riche
Chez Rene
These are all very well known ones and they are scattered all over the city in the different arrondissements (districts). But if you happen to strike up a conversation with a Parisian, ask him what Bistro he goes to on a given night.
One more thing that helps in Paris. Keep in mind that being a waiter is a very noble profession in Paris. Its not like America where your waiter is probably an out of work actor moonlighting for some bucks.
So when in Paris, ask his advice and treat him like a respected friend. In the Bistros the waiters will be pretty young and informal, but they still see themselves as professional waiters. When you treat them right, you will be rewarded with good service, very helpful advice, and you will get a pass on your bad French. In fact, the younger waiters might want to practice their English.