Driving in Paris can be akin to an amusement ride - fast and furious, only without the amusement. People here are busy with places to go. Not speeding, obeying regulations or parking legally are not necessarily priorities.
Parking tip: drop the car off at a car park outside the centre and take public transport. Or search here for car parks in Paris. Enter the city name or the exact address where you need a car park. Bonne chance!