Wow, so jealous!
For Normandy, I’m assuming you’re going there for the history, and learn something about Dday and WWII? If so, I highly recommend hiring a guide. They’ll take you to the beaches, the American cemetary, to St. Mere Eglise, and walk you through the background leading up to the day, and then the battles that happened on the day itself. It was such a memorable experience for us. We used: First Normandy Tours (recommended in Rick Steves book), and did the one-day American tour.
For Paris, a couple of recommendations:
Paris by Mouth food tour: Neighborhood food tours - you pick your date and which neighborhood. They’ll walk you around the neighborhood and stop at different shops - patisserie, macaron store, cheese shop, bakery for bread, meats and pates, wine. At each stop the guide will give the group a talk about the different foods and the group picks out some items at each place. Then at the end you go to a wine shop and feast on all of the spoils. I put this first for a reason, as this was one of our favorite experiences. I recommend it to everyone, and everyone has given it great reviews.
Bike About tours: Great bike tours from a smaller company. We did a Versailles Tour - awesome. Stopped at a market in the morning and picked up food for a picnic, then did a bike tour of the Versailles grounds - had a picnic by the water. Then tickets to a tour of the castle.
They also do a really good bike tour of Paris - stopping by different monuments and areas- nice way to see a lot of the city and learn a little something.
Bateaux Parisiens: This was a lunch/dinner cruise of the Seine. We did lunch, and thought it was great. Kind of expensive though, but a really fun treat.
Chez Janou - great restaurant in the Marais neighborhood. We always recommend it.
Hotel Des Grandes Ecoles - wonderful little hotel right in the heart of the Latin Quarter. The best thing about it is it has a gorgeous courtyard where you can sit in the morning and eat breakfast, and come back in the afternoon and open a bottle of wine. It feels out of the way even though it right in the heart of the Latin Quarter. Overall, I’d recommend getting a VRBO, but if you wanted a hotel, this is a good one.