The permit to hunt the wolf came into force on Monday and stretches to September 19th, according to the local Var Matin daily.
The decision to order the hunt has been described as a last resort in the battle to protect livestock from the predators.
"We have reached the final stage," Var prefect Paul Mourier told the newspaper.
"The various protection measures and defences implemented over the past few years have not been enough."
In the seven months to July 31st some 201 animals have died in a total of 85 wolf attacks in the Var, which is in the Provence-Alpes-Côte d'Azur region in the south-east corner of France.
The decision was taken after a recent acceleration in attacks, with a further 72 sheep taken in an attack on Friday.
The Var is the second department to recently allow a wolf hunt, following a decision by the prefecture of the Hautes-Alpes after a similarly bloody 2012.
According to the Francetvinfo.fr website some 216 animals have fallen victim to 62 attacks in the department.
Some 99 percent of the attacks in the Var have taken place in Canjuers, although the hunt has also been allowed in the municipalities of d'Aiguines, Chateaudouble, Comps-sur-Artuby, La Roque Esclapon, Montferrat and Mons et Seillans.
France's wolf population has grown to around 200 animals since being re-introduced in 1992, mainly in the south-east but also scattered across the Pyrenees.
Only six animals have been legally hunted since 2004.