Ice cream at Berthillon’s on the Isle St. Louis even if it’s cold and dreary.
I spent 10 days in Normandy eons ago and did not run out of things to do. I highly recommend going to the beach at Etratat (the stones are all geodes!) and admiring the rocks that Monet painted. My brother and his wife did the cliff walk that starts there as well and really enjoyed it. Visit Etretat - Normandy Tourism, France Pointe du Hoc was our favorite of the battle sites, there’s enough of the fortifications remaining that you can really imagine it. Don’t miss the Bayeux tapestry. Agree with trains for long distances.