A new strategy unveiled by the centrist government of President Emmanuel Macron will enable the number of wolves to grow to 500 by 2023 compared with an estimated 360 now.
Hunting wiped out the grey wolf in France during the 1930s and they only returned in 1992 via Italy -- currently home to around 2,000 wolves -- before spreading into Switzerland and Germany.
The regeneration of the population in France has led to tensions between the government and farmers in the Alps and Pyrenees mountains who complain that attacks on their flocks cause major financial losses.
Hundreds of sheep were let loose on the streets of the city of Lyon in November last year in one of a number of protests against the wolf, which has protected status.
Wolves on the move
Under the new plan a total of 40 wolves can be hunted in 2018 between September and December to keep numbers under control, while farmers will be authorised to shoot at any time if their flocks are under attack.
The 100-page strategy document will enable livestock owners to apply for state funds to shield their animals, but it will make compensation contingent on them installing fencing and taking other protective measures.
From next year, 10 percent of the total population can be culled but the proportion could increase if the number of attacks is found to be higher than expected.
Wolves eat between 2-4 kilograms (4.4-8.8 pounds) of meat a day on average and the predators have been blamed for an explosion in the number of livestock attacks in mountainous areas.
A total of 10,000 sheep were killed in the Alps region in 2016, according to official figures from the regional government, but the wolf is also known to feast on deer, wild boar or even domestic animals.
Damages paid out to farmers from the state for livestock killed by wolves rose to 3.2 million euros ($4 million) in 2016, up 60 percent compared with 2013.
Jean-Marc Landry, a wolf specialist, said one of the problems for the French government is that wolves are highly mobile and quick to move into new areas beyond the Alps.
He said they had already been sighted in the Massif Central area in the middle of the country where France's biggest sheep breeders are based.
"The question is not whether we want the wolf or not -- it's here," he told AFP. "We need to think about a third way, to find ways of co-existing together."