Hi Sonia,
Assuming that you have the black 7 pin socket on the back of your car (correctly referred to as the 12N connector) - you should see 7 copper coloured pins (or sockets) - then this only has intermittent power - for things like turn signals, brake lights, etc., and in any case the wiring is only rated for low currents - enough to run lights.
Charging the battery needs a few amps, but the fridge needs 10 amps or more - so heavy duty cable is used to supply this - and it needs to be "always on" unlike the lights.
So you need to visit a tow bar fitter and have the 12S socket fitted if you have a 12N socket.
If you are lucky enough to have the (superior) 13 pin ISO 11446 connector on your car - this already has all of the correctly specified wires in place - in which case have the camper sockets changed to a 13 pin plug - or buy a 13 pin ISO to 12N+S adaptor.
The 13 pin ISO socket (standard on many new cars) is waterproof, secure - with a twist lock, corrosion resistant, and was designed to handle the high current demands of appliances like fridges.
The much older 12N+S connectors were not designed to handle high currents and you need to take care that it is kept clean, and provide a good contact - otherwise you may notice that the plug and socket gets hot.
Fitting an adaptor is OK, but you have just introduced the deficiencies of the 12N+S system into a correctly designed connector - which is why I don't like this retrograde step.
Robert