Upvote:6
The main page relevant for EU (from France) and rabbits in English can be found here:
It contains a link for an English pdf, where rabbits (not intended for food production) is explicitly listed.
Short summary (from pdf) :
When entering Austria, private persons may bring any of the listed animals without a Health Certificate.
The animal may not be sold or given away to other persons.
The owners are advised to insure that the animal cannot spead any animal diseases and checking with a local official veterinary about current conditions.
The German page contains the same information.