Ordinarily I would never recommend to people that they visit Paris by car, but in August the situation is different. Firstly the roads are quieter, and secondly - and perhaps more importantly - 87% of the parking spaces in the city are free of charge for the whole month.
In order to avoid any nasty surprises though, you need to know about the other 13%! Generally these are the parking spaces on the busiest roads and in the most touristic areas, but just to be sure, make sure you check this complete list. (a PDF document in French. Payant = with charge, Gratuit = without charge!)