Carnets are an identity card issued by associates of the FICCs [Federation of International Camping Clubs] that effectively indicates you are a bona fide member.
Physically they are a bit of thin plastic, credit card size.
They are issued by organisations that are FICC associates so here the CC and C&CCC are examples.
You don't need one travelling in France; however they serve the same purpose as a passport proving your identity to a site owner and giving him the assurance you will pay up. You might therefore be asked and expected to lodge your passport or pay in full on arrival at sites, whereas we just leave our carnet with the site as assurance until we pay and leave.