I assume by French Police you mean the Gendarmes. What they call random checks are regular here; at least twice a year we will be stopped for paperwork check and breathalyser you must carry your insurance, log book (carte gris) and driving license (there is not an option to produce them later). Breath tests are common and by random they mean everyone on the same road. If they were stopping campers it is for the above plus weight check, they have a computerised system and weigh all four wheels, two at a time. Overweight means a fine and points! If you can't pay they will follow you or take you to a cash point. Plus you have to reduce the weight immediately.
If you have a radar warning device that will be confiscated and you will be fined. They are very tough now on speeding (in order to reduce road deaths) they have binoculars fitted with radar that checks you speed a long way from where they are hiding. So especially keep to 50kmp (30mph) within villages and towns.
Apart from that they are really nice folk!