Do not - under any circumstances - drive in Paris. I'd sooner drive through Times Square on New Year's eve.

That said, here are some suggestions for Normandy
1. Caen - you can walk through the Chateau of William the Conqueror where he planed his invasion of England in 1066. I did that daily on my way to university classes many years ago. Also, you may be interested in the D-Day Memorial museum there. Very impressive and informative
2. Mont St. Michel - Even though it is touristy with schlocky souvenir shops, it is still a place where you can step back in time (15th Century or so). Don't sleep there, but do walk up to the Abbey on the top of the Mont. If you get there when the tide rushes in or out, it is a fascinating thing to watch;
3. Bayeux - Walk around the village, but plan to visit the Bayeux Tapestry - depicting the Battle of Hastings in cloth. English speaking ear pieces are readily available and inexpensive;
4. By all means visit the iunvasion beaches at Normandy. Although somewhat crowded in June, it is a fascinating place and is almost impossible to comprehend what went on there in 1944.
5. Please visit the American Cemetery on Omaha beach. The beauty and respect of the place is breathtaking and awesome. My wife and I came away with tears in our eyes.
6. Spend a night or two in any town along the coast that does not cater to tourists.
7. Turn in your car before you get within 25 miles of Paris.

Enjoy your trip