Each driver must have Third Party Liability insurance for his vehicle on the circuit. It is the responsibility of each driver to check with his vehicle’s insurance if it covers damage caused to third parties resulting from practice, with or without timing on the circuit.
The green card of your insurance is not a proof of insurance.
On the other hand, in 2014, the FFSA has declared that licensees taking part in driving with non-licensees will not be covered by their Traffic Civil Liability licence.