I particularly like the Hotel Meurice, although since the refit you may not get one of the best rooms with a view over the Jardin de Tuileries at the price. Certainly worth asking though.
I usually stay at the Ampere when visiting for the Arc racing. Rooms are smallish but modern and comfortable. The main thing is, it is quite central, is surrounded by really good restaurants (I particularly like Phoebe's) and most importantly.... the room rate won't break the bank.