Best mode of transportation London-Bath-Normandy-Rouen-Paris-London

Have you considered the Eurostar from London to Paris under the channel? I have taken it several times and always enjoy the experience. Plus, it is a very quick journey from city to city.

Do you need a rental car in England? The itinerary you’ve mentioned sounds like it can be done via trains and buses. Bath has many trains from London, and Stonehenge can be reached via train to Salisbury and then a bus or taxi.

Could you pick up a car in France at the port you arrive in and then drop in France before your stay in Paris? Then take the Eurostar back to London.

For an international rental, apart from a huge international one way drop off fee, will you even be allowed to do it?
Bear in mind that you drive in France on the other side of the road, so the car is the wrong way round.
Although your whole UK itinerary could easily be done by public transport, if you do require a car in the UK it will almost certainly be cheaper to drop that car in Portsmouth, then to rent another at whichever of several possible ports you land at in France, then drop it somewhere on the outskirts of Paris (CDG or somewhere else), then Eurostar or fly back to London.
Again Eurostar is the best solution, as opposed to flying.

This is your first post ever on this board, and you haven't filled out the "home" field of your public profile. So we don't know how much choice you have in air tickets. But it's usually wiser to buy an open-jaw ticket, like [Chicago]-London/Paris-[Chicago]. It's a real pain to cross the channel twice. What is your month of travel? Total nights of the trip?

Did you check that your car rental will permit ferries. My rentals (not in England) generally have prohibited ferry usage. I agree that a car is useful in Normandy, but it may be an unnecessary hindrance for your other destinations in France.

I have not taken the ferry, but my wife got seasick when she did. We flew from London to Paris once, and these days, we use Eurostar. You may want to check on ferry customs and immigration time, because it's up to 90 minutes before Eurostar departures. That is, the Eurostar formalities are in the departure country, not in the arrival country.

You might use the Search box to find some threads about the Ferry trip. Example:
https://community.ricksteves.com/travel-forum/england/travel-canterbury-to-france-by-sea

I would not rent a car at all for this itinerary. I think a car for this itinerary will be more trouble than it is worth. Take a group tour from Bath to Stonehenge. If using public transportation, you will need a small amount of luggage since you will have to handle it yourself. However, rental cars also won't have a lot of room for luggage.

Are you happy to drive on the right in France in a car with a steering wheel on the right? Will your renter permit it? Will you have all of the equipment French law requires which UK law doesn’t?

In short take the train.

I’m not sure you can even take a British rental car to France. In any case it will be far cheaper to rent 2 cars: one for England and 1 for France. It’s expensive to take a car on the ferry, although I do remember that some of the ferries are restricting foot passengers so that could be an issue.

Public transport in Britain and France is pretty efficient except for rural destinations. I would fiddle with schedules so I only rent a car for a day or two in each country. A substantial saving may be possible flying into Britain and home from France on a single multi-destination ticket, bought using a multi-destination search function. You could save both the cost and the extra time of returning to your arrival airport to go home.