quickest way to get from Paris' Gare Montparnasse to Paris" Gare Lyon

It may depend on how much luggage you have. If you have a lot, it may be difficult to manage on the metro, since there will be a lot of stairs. If so, you could take a taxi - there should be some available outside the Montparnasse station. If you do not have a lot of luggage, you could take the metro. I am not sure which line, but you could look it up. Peter

Those aren't the easiest two stations to connect by Métro.

Leave plenty of time because Montparnasse is a very large station with a couple of extension stations as well. Gare de Lyon is also large, in two distinct areas.

There isn't a direct Métro connection. You could get the 6 direction Nation Métro (green) and take it towards Nation 11 stops to Bercy and either connect to 14 direction Saint-Lazare (purple) and go one stop to Gare de Lyon, or go upstairs at Bercy and walk it.

I've not made the connection at Bercy - perhaps somebody who has will pipe up.

That is one L-O-N-G day of travel you have planned. It is about the same distance as diagonally all the way across Texas.

Time of day matters and amount of luggage matters and depending on those details, the manner that I suggest would be to either take a taxi or Bus 91.

I like both trains and driving, and your plan is probably the fastest, but not great and not cheap, even with advance-purchase train discounts.

It would be an equally long day to drive directly from Pontorson to Arles, maybe 11 hours, and not without costs for gas, tolls, and the effort of the driver(s). But if you'll use the car in Provence, then I'd consider keeping the same one and splitting the drive over two days.

Another possible train route option would be to drive further and drop the car at Angers or Le Mans. On some days, there's a TGV following this schedule (and requiring a connection in Nimes to reach Arles):

Nantes
dep 09:02

Angers St Laud
arr 09:41
dep 09:44

Le Mans
arr 10:22
dep 10:33

Massy TGV
arr 11:22
dep 11:25

Lyon Part Dieu
arr 13:30
dep 13:36

Valence TGV
arr 14:11
dep 14:14

Nîmes
arr 15:01
(departs 15:04 to continue to Montpellier)

Gare Montparnasse is big and confusing but there is an indoor taxi queue if you can find it -- the problem is Paris traffic between those destinations. I would take the metro as it will be faster but that means everyone has to be pickpocket proof and also be able to manage the luggage up and down stairs. We have sat in bumper to bumper traffic using a taxi across town from Montparnasse -- I'd not want to do that with a train to catch.

This map https://www.gares-sncf.com/sites/default/files/field_plan_files/2018-12/plan_hall2_n3.pdf shows where the indoor taxi stand is located.

In answer to Nigel's suggestion, I can advise that the change between the 6 and the 14 at Bercy is rather easy. Except for the first few steps up from the 6 to the station level, the rest of the way back down to the 14 is all escalators. Nor is the distance between the two very long -- although there is a bit of a squeeze to get through part of the station as there is construction going on so part of the walkway is blocked off.

Thanks, Kim

Do you think it is easier on foot from Bercy or better to take the one stop on the 14?

Hmmmm. I would probably just go on the metro. At least in the metro, there are signs indicating the correction direction, whereas exiting a station to the street, one can find oneself very disoriented and waste time going in the wrong direction.

(I.e. a local — or someone who's been several times before — who knows the neighborhood could probably make good time on foot, but a new visitor would, I think, almost invariably take longer, spending extra time and energy.)