1.Five extra days in Rome is barely enough.
2. You need two weeks to visit your list.
3. Choose Bayeux over Caen, no comparison.
4. Giverny is on the way from Paris to both Caen and Bayeux. We stayed near Giverny , then Honfleur, lastly Bayeux.
Check the trains as we had a rental car that we picked up in Paris.

Thank you Suzi!

Of your list of French towns, Lyon is by far the most centrally located and easiest to get in and out of by air or train. Lyon is the 2nd/3rd largest city in France (depending on who you ask!) and has an easy to use metro. You could easily spend a week there and only scratch the surface! There is a gorgeous old medieval area to walk around and see les traboules, the passageways that helped the French Resistance evade the Nazis during WWII (Lyon was the heart of the French Resistance). From there, visit La Croix-Rousse, where the silk factories manufactured all the silk for the King of France (there's a silk museum if that interests you). The beautiful cathedral of Fourvière offers a gorgeous panoramic view of the city, with its two rivers and seven hills (like Rome!). Close by is the impressive Roman theater: Lyon was the Roman capital of Gaul (now France) and Roman ruins are everywhere. Aside from history, you'll find museums for just about any type of art/design. And let's not forget that Lyon is also the capital of French gastronomy, so excellent restaurants abound, including les Bouchons, the small family-owned restaurants in the old Lyon. I would also highly HIGHLY recommend a day-trip to Pérouges, a complete medieval village that is one of the official "Most Beautiful Villages of France." You can get there by train (about 30-40 minutes from the central train station of La Part-Dieu for $20 round-trip). I hope you end up visiting Lyon! Have a great trip!