From my experience, it's been horrible. Was at Orly Airport catching a flight to Strasbourg with AF with an avios car rental booking through BA. Flight was cancelled, called Avis at Strasbourg, no response, went to the Avis desk at Orly, he couldn't help us cause of communication difficulties, totally useless. Called another company at Strasbourg to try and alert Avis that we wouldn't make it that evening as we had to take the last train to Strasbourg instead. They said that there was no one sitting at the Avis desk. So the next day we arrived at Strasbourg to pick up our pre-paid car and imagine that famous scene from Planes, Trains and Automobiles, exactly that. It was cancelled. Wanted 250 eur a day for a new car, walked over to Europcar and got another for a cheap price. Claimed from BA on the way back, weeks of hassle and argument to get our money and avios back through something which was of no fault of our own. Got it eventually, but I'd never suffer that hassle again.

Moral: If you miss your car rental time, they'll cancel it and try to charge you more.