Hired car CDG to Giverny? Hotels in Rouen?

I do not know the answer to many of your questions but for the answer about leaving your bag at the ticket office (assuming you are going to Monet's house and gardens) see: https://claudemonetgiverny.fr/en/useful-information/#securite. Scroll down to "Safety and anti-terrorism measures." The answer is no.
What is your budget for the car service?

There is no luggage storage at Monet's garden, or at the Vernon train station. There is a storage facility listed on Nannybags (for a fee) near rhe station.( I think it's at a restaurant) I looked at the Daytrip site for a private car and driver, and the cheapest price for a sedan was just under €200. I wouldn't be surprised to see higher prices in summer.

For hotels in Rouen, look at booking.com and filter for budget and location. For car rental, have a look at AutoEurope for available agencies.

You can rent a car at the train station in Rouen. I wouldn't pick up the car until you are departing Rouen though; as the city center is walkable and there is no street parking in the city center as it's all permitted/limited parking. There are 24 hour parking garages though. We stayed in an Airbnb which we really liked. So if you do pick up a car while still staying there and go the hotel route, make sure it accommodates car parking.

Personally, after an overnight flight and then visiting Vernon, I'd stay the night near Giverny; leaving your bags at the hotel; then move on to Rouen.

Right before covid (around 2020) we rented a car in CDG and drove to Giverny and spent the night at a small hotel/restaurant (Hotel Restaurant La Musardiere See www.lamusardier.fr . It was great. No elevator. The next morning we toured Monet's garden and house before a late lunch at Rouen (La Couronne, See www.lacouronne-rouen.fr We had to drive thru Paris to get to Giverny. Easy trip but I was very tired driving because we had just arrived at CDG from the U.S. French roads aren't hard. I do not speak or read French. I had intended to take northern route to Rouen and stop by a small neo-lithic cite but went to Paris center by mistake. A little harder but not impossible. We eventually returned the rental car to the train station in Rouen after visiting several days in Normandy. The Train Station is not in the center of Rouen but a few miles from the center. Still in the city. The train station will take you to Paris and I do not know where else.

KD has an excellent suggestion and the safest: checking into accommodations in Vernon or Giverny where you can leave your luggage and travel to Rouen the next morning where you rent a car. What a glorious way to spend a jet lagged day, in this garden. Then you can get a good night’s sleep close by.

Thank you everyone for the suggestions, especially the ones that challenge a traveler's plan into a better idea. We've only hired a car once before and it was in a far cheaper country many years ago. What a surprise to see the estimated price, given by one commenter, for what is essentially a one hour journey but there it is. Perhaps instead we'll hop the train from CDG into Paris to get the train to Vernon since the Giverny gardens will not be open anyway for a few hours after we land. We had considered staying in Giverny or Vernon overnight the first night but wanted to get to Rouen by train and not "waste" the afternoon after we toured the gardens. That way, we would be in Rouen waking up in the morning, rested and ready to see the Old Town on foot. We are familiar with jet lag the first day of a trip but will not be driving to Rouen. We may also further investigate if there are places to leave a bag while touring the gardens, aside from having a hotel reservation in Giverny.....Thank you RS travelers! What a helpful forum. Really appreciate it.

There is (or at least was very recently) luggage storage in Vernon through NannyBags. I believe that it is at a restaurant on Rue l'Horloge near the station.