The lethal infection has affected 28 farms in the Hautes-Alps region in south-east France for the first time since 1992.
The first case was found at the end of June in the village of Montgardin where it killed six cows.
Since then, 50 more animals have died but there has been no evidence to suggest it has been transferred to humans.
Anthrax has the ability of killing cows, horses and sheep within hours.
It has been identified as the most likely cause of unexpected deaths in livestock.
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French website, The Local, has revealed that vaccinations can protect livestock, but the drugs in Hautes-Alpes are in short supply as the laboratory in Spain in closed in August.
Senior Hautes-Alpes official Serge Cavalli said animals were being vaccinated at affected farms in the region.
Agnes Chavanon, senior regional official, said: “The state is in talks with its European partners to discuss the availability and purchase of vaccines”.
Mr Cavalli said animals were being vaccinated at affected farms in the region.
The signs of anthrax in animals include flu-like symptoms, coughing up flood, chest discomfort and a shortness of breath.
According to the UK Government, farmers who are concerned about anthrax affecting their animals should report it immediately.
No human has been affected by the infection so far according to the French authorities.
The farms that have been affected have been banned from production for at least three weeks while the farms are disinfected.
The disease has existed for hundreds of years and still occurs naturally in both animals and humans in many parts of the world, including Asia and southern Europe.
France is the UK’s biggest market for sheep exports, which is worth £61 million annually.
The country accounts for around 55 percent of all lamb exports.