registration on Saturday, start on Sunday
Personally I would not recommend sleeping in the car for two nights before the ride. I was lazing in a hotel room until 2pm on the day the ride started, and that allowed me to go through to 8pm on the Monday night, 550km from the start, before needing sleep. Possibly I could have gone further. I doubt I could have done that if I had slept in the car on Friday and Saturday night.
If I ride this year, I will probably get the overnight ferry from Portsmouth to le Havre (closer to rambouillet than Calais) on Friday night, sleep on the boat and have a 2.5 hour drive to registration, then I will book into a hotel, or maybe a campsite nearby.
You will likely also want somewhere to sleep at/near the finish. I would not want to to finish the ride, sleep badly in the car and then drive back home afterwards. (last time I finished at 1am). Possibly you could get a bed at the last control (Dreux?) to be a bit fresher on arrival at Rambouillet.
If you have a campsite pitch booked for the week, then leaving your car there should not be an issue.