The A Cupulatta park in Corsica reported the theft of 56 of the reptiles, which it is concerned will be trafficked.
The animals have distinctive black and yellow shells.
In a post on Facebook, park officials said: “These tortoises cannot be legally sold so can only be destined for trafficking.
“Even if they remain hidden, future births will be unsaleable because we are alone with their official documents.”
Officials are also worried they may have been taken by anti-zoo campaigners.
In either case, the park fears the animals could be dropped into the wild and “contaminate” wild populations with germs, because they have been in captivity for so long.
The turtles would also come into contact with new animals and people they are not used to.
The park thinks they could still be in Corsica.
Police are investigating, local prosecutor Eric Bouillard confirmed.