Here's a plan that I am toying with that might work for you or you can tweak. I have the same predicament.
Day 1 - Land Paris 8:30 then Train to Bayeux Pick up car
Day 2 - Bayeux - Rest up from Jet Lag - Wing it
Day 3 - Bayeux - Mont St. Michel
Day 4 - Bayeux - Guided Normandy Tour (Overlord)
Day 5 - Train to Burgundy/Beaune - long train ride via Paris, then to Beaune - Rest, Wine, Biking, Hiking, eating, etc - Maybe get car for adventures.
Day 6 - Beaune- Rest, Wine, Biking, Hiking, eating, etc
Day 7 - Beaune - Rest, Wine, Biking, Hiking, eating, etc
Day 8 - Beaune - Rest, Wine, Biking, Hiking, eating, etc
Day 9 - Paris - See Paris or any of day trips below
Day 10 - Paris (Possible Train day trips: Giverny, Fountainbleau, Provins, Epernay, Reims, Chatilly, AUVERS-SUR-OISE, Versailles)
Day 11 - Paris (Possible Train day trips: Giverny, Fountainbleau, Provins, Epernay, Reims, Chatilly, AUVERS-SUR-OISE, Versailles)
Day 12 - Paris (Possible Train day trips: Giverny, Fountainbleau, Provins, Epernay, Reims, Chatilly, AUVERS-SUR-OISE, Versailles)
Day 13 - Paris (Possible Train day trips: Giverny, Fountainbleau, Provins, Epernay, Reims, Chatilly, AUVERS-SUR-OISE, Versailles)
Day 14 - Back Home
Let me know what you think, the trip to Normandy really adds a wrench in there. Another option I'm looking at take me a little more south, and moves Normandy to a Paris Day trip. Adding in case you are interested.
Day 1 - Land Paris Train to Lyon - Maybe car while in Lyon
Day 2 - Lyon
Day 3 - Lyon
Day 4 - Train to Avignon - Possible day trips (Arles, Aix-en provence, Marsaille, Montpellier, Nimes) - Maybe get car but I think most of these day trip can be done by Train
Day 5 - Avignon
Day 6 - Avgnon
Day 7 - Avignon
Day 8 - Paris Possible day trips Possible Train day trips: Normandy is Mandatory, Giverny, Fountainbleau, Provins, Epernay, Reims, Chatilly, AUVERS-SUR-OISE, Versailles)
Day 9 - Paris
Day 10 - Paris
Day 11 - Paris
Day 12 - Paris
Day 13 - Paris
Day 14 - Back Home
Good luck, and excuse my spelling. Any feedback is appreciated.