Most foreign countries will allow you to drive on your US license for a period of time. For example, I am living in the Philippines and have been here many years. Here a person can drive on any US license for a period of 30 days from date of entry into the country before needing to get a Philippine License.
There is no reason to give up or turn in your US - California license before you leave there.
I would however call or email the French embassy closest to you to see what laws cover you driving in France with your license to play it safe.
Best of luck