Each family unit is entitled to bring five (5) animals with them when they move to France, but it will take preparation to travel and transport your pet(s).  

Every animal must be identified by a microchip or a tattoo. In the United States, you may acquire the microchip standard ISO 11784 on the web at: http://www.pettravelstore.com/ It should be implanted only by a veterinarian.

Every animal must have a valid rabies vaccination, even if the animal is less than 3 months old. If it is the first rabies vaccination for the pet, you must wait 21 days between the vaccination and departure.

A health certificate will be valid for 4 months after signature by an official veterinarian (certified by the USDA). A blood test is not required for animals coming from Canada and the United States.

You may bring a maximum of 5 domestic rodents. A health certificate (in French), executed not more than ten days prior to arrival into France by a national licensed veterinarian of the country of export must accompany each rodent.
 
You may bring a maximum of 5 pet reptiles per family, provided: they are not sold under any circumstances; they are accompanied by a health certificate executed not more than ten days prior to arrival and bearing the signature of a licensed veterinarian of the country of export; and are free of evidence of disease (in particular, of lesions of the skin).

WARNING: The EC regulations regarding the movement of pet birds have been modified in response to the avian influenza alert (bird flu). The regulations below remain applicable until further instructions.

Pet birds may be brought to France.  However, each family is limited to 5 birds.  Because of avian flu concerns, please see the following link for further explanations:
http://www.ambafrance-us.org/spip.php?article783