There are a number of very reasonably priced French bistros on rue Guisarde, which is the street at the end of rue Princesse. I have been to La Boussole a number of times.
la-boussole.com
12 Rue Guisarde
75006 Paris, France
01 56 24 82 20
Italian:
www.lalocanda.fr/
La Locanda
8 rue du Dragon, 75006 Paris - tel: +33 (0)1 45 44 12 53