This seems a cunning plan - been camping a number of times in France and have hired a fridge. Invariably, they just come round to the pitch and chuck off the back of a trailer a standard domestic fridge.
Usually with a dubious standard of cleaniness.
Proper camping fridges cost an arm and a leg, but I spotted in Currys a small Own Brand tabletop fridge for 60 quid. Seems the same build quality as the hire ones and is about the same volume as my Waco Icebox - and halve the price.
So be interesting to see if it stands up to the beating its about to get.
I'll be interested to hear how you get on. Theoretically with an inverter you could run it in the car whilst in transit - or would that kill a compressor fridge?
You could run it of an inverter in the car, but the inverter would need to be directly wired to the battery, the in car 12v sockets are only rated to either 10amp or 20amp so would blow in an instant.
We have never hired a fridge for our fortnight campings in the South of France, and since 2008 have taken our own portable fridge.
£60 for a Table Top fridge is a good deal, and should work fine, and as the OP mentions a massive saving compared to buying a proper portable fridge, although our Mobicool C40 was just £139 back in 2013.
Having said that we would not be without our icle Waeco CF25 portable 12/24v fridge, for the 1000 mile journey, although we did get lucky as it was a £150 bargain new back in 2008.
I picked up one of the 60quid fridges for our hols. We're in Provence just now & the temps have easily been in the 30's every day. One if the best purchases I ever made.