Many hotels are situated near place Denfert Rochereau. I recommend some of them below, but many others can also be very good:
For a cheaper solution you can also book a room at the FIAP Jean-Monnet, which is situated 30 rue Cabanis, 75014 Paris, at about 15 mn walk from the Observatory (Métro St Jacques). The single room is at 61 euros per night, including breakfast.