Sep.5 (GMM) Magny Cours has lodged an application to be considered for F1's 2013 calendar.
French language sources RMC, L'Equipe and AFP said the application was given to the country's sanctioning body FFSA this week.
The reports said Paul Ricard also intends to apply for consideration next week.
RMC claimed that while the FFSA did not comment, both Magny Cours and Paul Ricard propose to host one race every two years, in alternation with another country.
F1's governing FIA is expected to publish the draft of the 2013 calendar in early October.
FFSA president Nicolas Deschaux is quoted by L'Equipe as saying France will only return to the calendar if it can convince F1 chief executive Bernie Ecclestone.
"The commercial rights holder does not hear arguments of the heart," he warned.