Normandy: (You might make clear whether you mean more than just the D-Day Beaches)
Because (assuming the virus recedes) you will not be dealing with summer crowds, I urge you to consider renting a car. I agree with the first reply, and suggest that you will wast vast amounts of time waiting for busses (if there are any), and will be unable to visit some locations. If you post again, you might mention if there are physical or stamina limits on how much walking you can do, and whether you strongly prefer a paved walking surface. I would certainly carry taxi phone numbers, and budget for expensive taxi rides.
There is tremendous demand for guided tours, from people who are not staying long, those who want transportation, and those who want to have a professional guide experience. The demand keeps the price for D-Day tours WAY up, and makes them fill-up well in advance, with advance payment required. We didn't miss having a guide, because we had two or three travel books with specific chapters on that area (one of them Rick's.)
Having seen many professional guides around us, I can confirm that they provide a great deal of supplemental detail, like photographs showing long-ago views of the now almost pastoral sites of horrible battles. Like any tourist destination, if you don't do your own research and have a list of sites and routes, you may not get the maximum experience.
This area is also tough to do without your own car. Guides aren't quite as expensive as in Normandy, but the long distances involved make a guide experience take up a lot of time, which adds up to Euros! I would research in advance whether any Chateau hours are shorter in October, and have more days off.
We happen to like gardens, so I wouldn't say that October is an ideal time. But you will have might lighter crowds than we did in July. Parking at D-Day sights and at Chateaux required driving around lots more than once, and usually parking in an overflow lawn-parking spot, with puddles and ruts to negotiate.