We have just returned from France with our dog -- always go the shuttle, couldn't be simpler, no stress the dog just stays in the car,in bed, basket however it normally travels, can sit on your knee if it prefers no one is interested as long as it stays in the car.

Coming back you need to visit a vet more than one day and less than five before return, costs about 40 euros. At the terminal it is signposted to the dog check section where they will check passport and vaccinations etc - takes a few minutes, very straightforward, that's it. There is a doggy runaround area and free dog magazines.
Good luck!