May/June will likely be some combination of cool/windy/wet with a chance of nice weather in Normandie, so be prepared. Paris and Loire should be mostly nice.
Are you renting or leasing a car? IMO that will be your best bet, you will need a car in Normandie and Loire, and to get to Chartres from Loire. If not, everything becomes more difficult.
I took a similar trip in September except I added a loop through Brittany. I took a train to Rouen from Paris, walked around the center for a few hours then picked up a car to drive to Etretat. A week is a pretty good stay in Normandie, as you develop your itinerary you may decide to shave a day or so off to add elsewhere. I think you would enjoy the cliffs of Etretat and Fecamp. If you are interested in D-day, there are German defenses all over the tops of the cliffs. They were abandoned after D-day, rather than attacked, so they are still intact but mostly filled with dirt.
You have time to see Honfleur, Bayeux and explore Caen as well as see the D-day beaches. I really enjoyed the Bayeux tapestry and MSM because I like pre-Renaissance history most. My loop through Brittany included very old towns and prehistoric monoliths, cairns and dolmen(s?).
My first stop in Loire was Fontauvraud Abbey then Chinon - again for the earlier history. I traded my car for a bike in Chinon, which later led me to drop Chartres and decide on a train directly to Paris. I biked to Villandry to see the gardens, then to Amboise. While in Amboise I biked to Chenonceaux then saw Clos Luce and Chateau Amboise. I managed that in 3 full days (four nights). If I spent more time, I would have moved to another base further up the Loire, maybe Blois, and visited Chaumont-sur-Loire and Chambord. At some point, everyone gets maxed out on the Chateaux. I think you're better off picking a handful and spending less than a week. You can easily spend extra days in Paris and not see everything.
I do think a side trip to Oradour-sur-Glane is too far out of the way. If it's what you really want to see, however, you shouldn't rule it out based on my opinion. Use viamichelin.com to approximate the drive time there and to your next destination. If it were me, I'd make it part of a "loop" and plan on some things to see along the route rather than a drive straight there, presumably from MSM, then to Loire.