Automobile insurance is mandatory (Article L211-1 according to The insurance French code).
Automobile insurance is mandatory; each driver has to hold public liability insurance for his vehicle on racetrack.
It belong to the driver to confirm with the vehicle insurance if it compensates for damages due to the third party result from the practise, with or with out timing the racetrack.
The green card of your insurance cannot be a proof.
Permit you have subscribed with FFSA provides insurance in the event of injuries, but do not compensates for traffic public liability.
Check with your insurance if your physicals guarantees are due during you motor sport practice.