We always use Ezyshuttle. Out of interest I've just checked the TGV for our upcoming trip in February as there are only 2 of us travelling this time and thought it may be a bit cheaper and relatively simple to do as we won't have the kids with us:
The first train after my flight lands is 18 minutes after landing which I wouldn't risk booking, but even if I did it's showing full.
The next train is 1 hour and 17 minutes later. So even with the actual journey being only 10 minutes, I would be in Disney almost an hour and a half after landing. Then I'd need to walk or use the shuttle bus to my hotel, another 10 minutes maybe. With 2 adults this is certainly doable, but a bit of a hassle with kids, large suitcases/prams etc.
The cost for this journey for 2 adults is 52E.
I know that when using Ezyshuttle we'll usually be at Disney within 45 minutes to and hour after landing. Luckily our gate is generally very quick with passport control - I know this isn't always the case for everyone, and we'll only have hand luggage.
Ezyshuttle will be waiting inside the Airport as soon as we exit the baggage claim area, with our name. We'll go directly outside into a car, usually this is a people carrier type vehicle with 6-8 seats. Child seats are available if required and you let them know what you need before travelling. It'll take about 40 minutes to get to the Disney hotels and we'll be dropped at the hotel reception.
The cost is 70E (for up to 6 passengers). More expensive for 2 adults, but a much easier transfer.
We usually travel as a family of 4 or 5 and TGV would be more expensive than using Ezyshuttle.
On the return journey we'll be picked up from the reception at our hotel and dropped at the correct door to the airport terminal. They even give you directions on how to get to the security/check in area.
Countless trips with them now and always had excellent service.