There are many nice choices with reasonable rates (less than 250 euros per quadruple) if you're willing to look outside of chain hotels. Paris is famous for its independent little boutique hotels and there are many of them. Here are a couple reasonably priced, fairly centrally located hotels which I know. I checked the rates, they seem to be way cheaper (of course your exact dates will determine the price, these "from" prices can be deceptive a bit.)
Hotel Taylor at the Republique, quad from 162 €: http://paris-hotel-taylor.com/
Hotel Choiseul at the Opera, quad from 174 €: http://hotelchoiseuloperaparis.com/
These are nice mid-range 3-star hotels, and there are many other similar options for sure.