We are moving from the USA to Nantes, FR with 2 cats.
You want to make sure that you let the airline company know ahead of time. You cannot buy the tickets through a third party and add your cats later. At least, that is our experience. You also want to pick your airline carefully because some will let you have your cat with you (in the cabin) while others will not. It also depends on the size and weight of your cat. You must have approved container/bags to carry your animals as well. Again the best is to check with the airline, mostly if you want the cats with you. You cannot bring a kitten with you. There is an age restrictions. Click here for more info.
Also, some countries require a quarantine period. This is not the case of France but it is for other European countries (England) and so if you are changing plane, make sure that a quarantine is not required for that country.
We chose Air France because it was a direct flight and they let us keep the cats with us. Information here if you are considering using them.
For France, you will need to have your cat micro-chipped. There are two kinds, make sure to ask for the international one. You will need proof of vaccination and that must be done within three months of departure (at least as of summer 2016).
Once we have arrived, we will report back on our experience!