Transportation Help: Lourdes-Amsterdam-Hopsten-Paris (CDG)

For Lourdes to Amsterdam, unless you drive (which I would not advise -- it's a 1350 km/840 mi drive), you'll have to make one connection somewhere:

1. The closest major airport is Toulouse (180 km away, about a 2 hour drive). Toulouse offers nonstop flights (2h) to Amsterdam. If you can find and can afford a car service to get you from Lourdes to Toulouse, this would be my preferred option as this is likely to be the shortest time. (Without a direct car, you take the train to Toulouse city and then a bus or cab to the airport.)
2. There are smaller airports in Lourdes and Pau (12 and 55 km from Lourdes city center), but they do not have direct flights to Amsterdam, meaning you will have to change planes, most likely in Paris. If you opt for this, make sure your flights in Paris are at the same airport, i.e. do not select an itinerary that has you arriving at Paris Orly and departing from Paris CDG.
3. There are no direct trains from Lourdes to Amsterdam and the trip will not be short (at least 10h overall). In addition, even train times that claim just one connection in Paris really involve two, as you would have to switch from Gare Montparnasse to Gare du Nord in Paris (it's not a complicated trip, straight shot on the RER B, but still another connection to navigate). I don't see this being a competitive option unless you are afraid of flying or just really, really love trains.

Quite frankly, no matter how you do it, this leg will take you the better part of the day as I don't see it being any shorter than 6 hours overall.

As for the Hopsten legs, will you need a car in/around Hopsten? (It seems like a smaller town, so I'm not sure what you have planned.)

If you do need a car, I would consider renting a car at Amsterdam Schiphol airport and driving to Hopsten (225 km, a bit over 2h). Then on the return I'd drive back to Schiphol, return the car, and then get a Thalys nonstop train directly from Schiphol to Paris (3h).

The reason I suggest picking up the car at Schiphol is because it has both many major car rental facilities and a direct train to Paris (there is a railway station directly at Schiphol). The other place that offers this is of course Amsterdam Centraal station, Amsterdam's main station, but it's smack-dab in the city center and I would avoid driving those small city-center streets if you don't have to.

The other option would be to drive directly from Hopsten to Paris (675 km, at least 7h) and find somewhere to return the car there, but then you would have to consider cross-border and one-way fees, which can really add up.

If you don't need/want a car in Hopsten, there are nonstop trains from Amsterdam to Rheine (2h40m), from where you'd probably have to get a cab for the 20 km to Hopsten.

For the return trip via rail, you'd have to get to Rheine and then make a connection somewhere, probably in Cologne; the entire trip is likely to take at least 7h. I don't think there's any option for Hopsten > Paris that involves air travel that makes sense. However, Germany is the country I'm least familiar of the three you've mentioned, so someone else may have a better idea for non-vehicle options between Hopsten and Paris.

Thank you to both of you for your great information! It is so much appreciated. I rethought my plans based on the input received here.
I booked a non stop flight from Toulouse to Amsterdam and even with hiring a private car to drive us to the airport in Toulouse, it's only $40 more than the other locations and will be a much easier trip.

Then I was able to book a car in Amsterdam to drive to Hopsten as well as booking a flight from Amsterdam to CDG. Since our hotel is right there, it will be so easy and convenient.

I am so relived that our plans are solidified and that this will make the travel so much easier on my mom. Many thanks for your expertise!