Your permit compensates for automobile public liability for vehicle used on accredited racetrack, but do not insures the driving out of it.
It also includes, the lowest physical protection of the driver.
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.
Check with your insurance if your physicals guarantees are due during you sport practice