The bad news is that student residents are often oversubscribed, so make sure you make your application well in advance (at least several months). Ask your current or future university for information and help on this process.
In summer, during the main holidays (July-September), some residences also offer short-term rental rooms at good prices.
French Universities offer accommodation (both rooms and studios) at good rates (sometimes as 'little' as €120 per month outside Paris). These residences are called Cités-U and are managed by CROUS, which are the regional branches of CNOUS, the national student service agency.
As the gap between demand and supply is extraordinary wide (especially in Paris) this accommodation is often given out on social criteria or reserved for scholarship holders or exchange program students. You can find further information on the respective websites of the organizations:
A list of other CROUS agencies with their contacts can be found on www.cnous.fr, at the bottom of the main page.
Private residences are obviously more expensive than the accommodation provided by CNOUS, but usually offer still very good deal. This is the list of a few organizations:
Résidences Estudines has facilities in thirty major French towns, with prices between €450 and €800 - www.estudines.fr.
ADELE (Association pour le Développement Économique du Logement Étudiant), the Association for Economic Development and Accommodation of Students, runs a nice website with student accommodation available in some 100 French towns - www.adele.org.
CLEF (Centre de Logement pour Etudiants de France), the Center for student accommodation in France, has its facilities in Grenoble (Montesquieu and Saint Exépury), Rouen (La varende) and in Evreux (Charles Péguy). The rents are between €200 and 300 - www.logetudes.com.