Not mentioned so far on this thread - by far the most common reason for a ramp-check on an N reg aircraft in France is to check the VAT (tax) paperwork. Any aircraft that is resident in Europe and therefore in what is called "free circulation" in the EU must have "imported" the airframe at some point. Locally based N reg aircraft understand this, and will have imported the aircraft, paid the tax (and if they know what they are doing, claimed it all back again). Itinerant N-reg aircraft can get caught out - if you overstay your welcome, you become liable to pay the tax.
The French "Marigolds" will therefore ask to see all your aircraft papers - in fact they will start with the tech log because they want to see if you have done intra-European flights, and how long you have been around. They will then work down the ownership, licences and so on.
If you are in a hurry, and you HAVE imported the aircraft into the EU properly, then in my experience you can short circuit the whole nonsense by just handing them a copy of the VAT receipt as the first item... They immediately lose interest and you can go on your way.
The reason is simple - if they catch anyone, they get a bonus of a percentage of the tax, and on a small Citation the tax might be the best part of a million dollars.