There are no readily available police statistics for car crashes sorted by location in Paris. My bet is: less than one car crash on average any given day.
You could attempt a guess based on these few facts: (source: Préfecture de Police - bilan Sécurité routière 2011)
- in 2011, 6,423 car crashes (not including bumps and minor collisions, which may go unreported) occured in Paris proper;
- the daily average is then 17.6 car crashes in Paris proper;
- even though the Arc de Triomphe sits on a very busy roundabout, there is just a tiny (very tiny) fraction of the traffic in Paris passing there.