Train travel

There is no luggage check for trains. You are responsible for getting it on & off the train. There are luggage racks at the end of the car for large bags & overhead racks for smaller bags. There are no restrictions - just what you can get on & off - there are no porters.

True, no checking of luggage on trains. You have to hoist it yourself. Easier with smaller bags.

You don't need to check your luggage but you will need to lift it and lug it.

Here's a great discussion of the subject of luggage on European trains: https://seat61.com/luggage-on-european-trains.htm

Are you continuing on to Rouen right away? If so, you will have to change stations from Gare du Nord to Gare St Lazare. If you are staying in Paris for a few days, then good for you.

I just can't resist suggesting that you might want to rethink those large suitcases. Getting on and off and changing trains can be a nightmare with large bags because the entrances are usually crowded, there are steep steps and the time is short.

Many people travel for long periods of time with only enough clothes for a week. They do sink laundry in the room, do their own at a laundry, or have it done for them by the lodging or a laundry while they are out exploring.

There are lots of threads about packing light here and great information on that here as well. Sarah Murdoch is the packing light maven and her video is most instructive and inspiring.

"Researching train schedules I've found several to select from" - is that several trains or several alternative schedules?
"Researching the topic via the train website" - which train website?

The trains between Amsterdam and Paris are operated by a company called Thalys. It should be their website ( https://www.thalys.com/nl/en/ ) you are looking at for times, prices and buying tickets. A reseller may only offer some of the trains, and/or may charge more. There is one departure every hour from Amsterdam to Paris, you have a good choice.

It sounds like you have not travelled by train and are expecting an experience like airports, that is not the case. There is no check in, it is your responsibilty to get yourselves and your luggage on the train before the doors close and it leaves. There is nobody to assist, but plenty of signs.

Please do not dismay. While train travel may be different than you expect it is a great way to travel and far more convenient than flying. While you are responsible for your own baggage you do get to avoid the cattle treatment of airports - no security lines, no boarding lines, traveling to & from the the airport which is generally outside of the city. Instead you are comfortably whisked from city center to city center with a great view of the passing countryside. We frequently enjoy a glass or bottle of wine along the way along with a picnic or snack.

While you certainly would not need to convert to a carry on bag only you might consider paring your luggage to a size easily handled. Our first trip - many years ago - we had FIVE bags plus personal items for the two of us! It took boarding and exiting one train to realize that was not going to be fun! I sorted and we left the two largest bags in a locker at the train station for the duration of our trip.

Some tips:

Arrive early enough to find the car placement plan on the platform - this will tell you where to stand for your car. When the train pulls in be ready to board - be standing right behind the line with bags there. A few minutes before arriving make your way to the rack where your large bags are and pull them down - move into the area where the door is with all of your luggage to be ready to exit the train. If the door does not automatically open there is usually a button that will open it nearby.

We now travel with a 22" bag and a smaller bag that rides in top of it - no matter how long the trip.

Actually, German Rail runs a baggage service (Gepäckservice) where they will pick up your luggage at your home or hotel and deliver it to a hotel or your home. Cost is 17,50€ per piece and direction. Here is the German language page. I think Swiss Rail has a similar service; I don't know about Thalys, but on German Rail, the earliest delivery is 3 days after pickup, which probably wouldn't help you.

When I was in college (1960s), I used the trains to get from my home on the west coast to the college on the east cost. At that time, you had to take the luggage to the train station at least three days in advance and pick it up at the baggage room of the train station where you got off.

I so appreciate all of the suggestions. We are meeting our daughter in Amsterdam when she completes her study abroad program and after a few days in the city will depart to see some sights she's interested in. Years ago my husband and I rented a car in Nice and spent several days exploring the south of France and ventured into northern Italy. Our daughter wants to visit St Mont Michel and as a daughter of a WW2 airman I thought as long as we're kind of going that way we could visit Normandy. Reading articles about travelers difficulty renting and driving cars out of Paris we thought it might be best to travel into Paris, switch trains to Rouen where we could rent a car and set out for a few days. We will return to Paris for a few days, although our daughter states she has no desire to see the city, before moving on to Lisbon.
Does this seem doable? Should we take the train to Lisbon or fly? We have a total of 10-12 days total travel time upon our arrival in Paris.

Getting from Gare du Nord to Gare St Lazare, which with a lot of luggage, probably means taking a taxi. Be sure to use the official taxi line.
An alternative is to travel from Amsterdam to Lille Europe and rent a car there, then drive straight across northern France to Normandy, bypassing Paris all together. Then you could drop the car in Caen before taking a train back to Paris.

Going to Lisbon, I would definitely fly.