Parking in Paris???

You are going to spend between 20€ and 40€ per 24-hour period to park your car. Is it a rental? If so
have you considered turning it in and renting another? There are lots of pay parking lots in Paris. What area of town will you be in? Indigo, previously Vinci, has lots all over town: http://www.parkindigo.fr/en/

From which direction will you be driving in to the city and where do you need to be? There are a lot of options, some of which are much easier to drive to than others.
Have you driven in big European cities before? It can really be difficult and take a lot more time than you think it will. Paris is particularly hard due to many one-way streets, extremely heavy traffic, non-existent lanes in many places, and a million other factors. I agree with the first poster that it might be better to return the car before driving into the city and then renting one again when you are ready to move on. It will cost you well over $100 to park for three full days.

yup, it's going to cost, unfortunately. sundays are still free. Anyway, on the street, you can only park for two hours at a time before you have to move. 4 euros an hour for street parking, for a maximum of two hours during the day.

Check out the hotels at La Defense. Some of them have below-ground car parks. I am assuming you do not plan to use the car while you are in Paris? There is good bus and/or metro service to central Paris from La Defense, which isn't the most picturesque part of Paris but a car is a burden and limits your options.

You don't need/want rental cars in big cities. Don't drive into Paris. Drop your rental car and then train into Paris. It's so much simpler and saves all kinds of headaches and Euros and peace of mind and etc!

I was impressed with the parking skills of drivers in Paris. They could get their tires tight against the curb with only a few centimeters of space between cars to the front and back. How do they do it?