Best Travel from Paris to Bayeux

The train is the best option in my opinion. Easy and fast. You can't check your luggage so you need to carry it yourself.

You don't say if you are only visiting Bayeux, or if you plan to see various D-Day beaches and/or museums? Do you know if your hotel is walkable from the train station? You are NOT going to Mont St. Michel or Le Havre? 7 people will need a very big vehicle, adding premium cost to an already pricey car service. Don't forget that you have to, in effect, pay for an empty return to Paris unless you are paying the driver and car to stay with you in Bayeux.

Normal European trains have luggage racks at one end of long-distance coaches. And a much narrower rack over the seats, which often can barely accept "carry-ons". There is no checked baggage. I don't think I've even been offered it on premium trains, like Eurostar.

If none of the seven of you have ever taken a European train, you need to do some research. Start here:
https://www.ricksteves.com/travel-tips/transportation
https://www.seat61.com/

Most posters on this newsboard favor trains, and they are not that hard to manage. But getting up the stairs (on occasions when the train floor is not level with the station platform) can be challenging for people with mobility difficulties. One test would be, can all 7 put their carry-on up in the airplane rack alone?

Thanks! We are staying 2 nights and are a short distance from the train station. We’re planning to take an organized tour to MSM and beaches. I’m just trying to find the best transportation out and back to Paris. I can handle my own suitcase but not sure the entire group is as capable. Thanks for the links

Sorry, I should have offered this as well:

https://search.ricksteves.com/?button=&date_range=2y&filter=Travel+Forum&query=Train+paris+bayeux&utf8=%E2%9C%93

Note that it's easier to train to Bayeux from downtown Paris than from the airport.

But getting up the stairs (on occasions when the train floor is not
level with the station platform) can be challenging for people with
mobility difficulties.

On the Nomad trains to Bayeux I think you can expect low floor trains.

I can handle my own suitcase but not sure the entire group is as
capable.

I would suggest they are taking too much.

Your use of "elderly" has me a bit confused. The term cam mean different things to different people! For instance, do any of your companions have mobility issues? I recently traveled Paris to Bayeux - I have a few thoughts.

I took the train from Paris St Lazare to Bayeux. Easy transport, fast, many departure time options. St Lazare is a major station with accessibility help:
https://www.garesetconnexions.sncf/en/stations-services/paris-saint-lazare/accessibility

Bayeux is a small station. On arrival, it is necessary to cross the tracks from the arrival platform via overpass to access the station proper and leave the premises. There is a small elevator - if my memory holds, multiple elevator rides will be needed for 7 with suitcases. I traveled with a carry-on and shoulder tote bag and didn't want to wait for the elevator - I managed the stairs carrying my bags. (I'm not sure if I fit your definition of "elderly"....)
https://www.garesetconnexions.sncf/en/stations-services/bayeux/pratical-info

Will you walk to your accommodation? Rhetorical question for you to answer, but consider that Bayeux is small. When I arrived on a mid-day train, there was one taxi at the taxi stop. It would not fit 7! If some in your party would prefer taxi to your lodgings, it might be wise to have the numbers of a taxi company in case there is no taxi waiting. I used the station on several other days - one day, in light rain, no taxi at all so I walked back to my hotel, about 25 minutes. My hotel called a taxi for me to return to the station for my departure. I don't know about Uber - claims to be available, but I didn't try it.

If the train seems too much, if you google "Paris Bayeux private transfer" you will see a number of transfer/shuttle companies with reviews. Perhaps someone on this board has used one if research gives you some options you want to explore further.

I am sympathetic with you in trying to arrange logistics for your group. I made similar plans that were canceled by Covid - my rule was carry-on only and must manage your bag with minimal help available. Frankly, I've not had the energy or desire to re-arrange and execute the canceled trip!