When I was on vacation there earlier this year, I drove right into the middle of the old walled city in Avignon until I noticed people giving me wired looks and a confused cop asked me how I got in there.
Out of curiosity I looked up Avignon on google maps, and sure the roads are skinny as hell but they exist and there plenty of cars. The whole place is viewable on Google Street View, presumably taken from a car. Maybe you were just in a restricted area?