Are you the only Cessna operator in France? If not, the DGAC and OSAC have already dealt with Cessna aircraft, and know how they want to define the terms. Ask them how they define it for other operators.
I know what they want, they want "block time".
If I want them to accept airborne time, I need a document from Cessna saying that their MM refers too airborne time.
In the meanwhile I got an email from Cessna saying that it refers to G1000 time, which is not far from airborne time.