The main difference between the two is the length of time that they remain valid for. Pet Passports are valid for as long as you keep them up to date with relevant vaccinations. However, an Animal Health Certificate is only valid for one trip to the EU, therefore you would need a new certificate each time you travel.
This can be done by a French vet, and in order to do so, you will need to provide details of your dogs' vaccinations and proof that you are staying in France for more than three months (i.e. your temporary long-stay visas).
You will need a Certificate of Veterinary Inspection to travel and some airlines require an acclimation certificate. Both of these certificates can only be completed and signed by a federally accredited veterinarian.
You probably have a plan for your own passport, but your animal companion needs one too. All pets traveling to and from the United States need a passport. Keep in mind, a “pet passport” in the U.S. refers to the extra documents you need to travel to other countries with your pet.
Creating your own pet's passportThe Annex IV for the point of entry (first) country you will be visiting (they are all different) completed by your veterinarian and certified by the State USDA veterinarian. Your pet's rabies certificate which must be attached to the endorsed Annex IV form.
Generally, airlines charge a pet fee of $100 to $200 each way, but prices will vary depending on where you're traveling and your airline. Check the airline's pet policy before purchasing a ticket to make sure your pet meets the airline's breed and size requirements.
Even though you can't buy an extra seat for your cat, you'll still have to make a reservation for it. Several of the biggest airlines in the U.S. charge $125 each way for an in-cabin cat. However, fees are somewhat less on other airlines, like Southwest Airlines ($95) and JetBlue ($100).
Most of the time, cats travel quite well without the need for medication. Some cats, on the other hand, experience tremendous stress when subjected to air travel. Consult your veterinarian to create the best travel plan for your cat if she does not travel well.
Usually dogs are only allowed to fly in the cabin—known as carry-on pets—if they can comfortably fit in a carrier that you can stow under the seat in front of you. A small number of airlines, including JetBlue, Alaska Airlines, and Etihad Airways, allow passengers flying with dogs to buy an extra seat for their pet.