The wolf had died out in France by the 1930s but returned across the Alps from Italy in 1992.
Now it is a protected species and 360 have been counted in France, up from 292 in 2016.
The government has a target of 500 by 2023.
But wolves are believed to have killed nearly 12,000 sheep in 2017, a rise of 2,000 on the previous year, so they are hated by many farmers.
Conditions for compensation
Breeders receive compensation for any livestock killed but the new plan has restricted the right to farmers who have taken at least two of the recommended measures - trained dogs, enclosure or night-time protection, electric fences and shepherds - to protect their flocks.
That change has prompted protests, including from about 20 MPs in the ruling Republic on the Move party who represent constituencies in affected areas.
An open letter addressed to President Emmanuel Macron and Prime Minister Edouard Philippe and signed by 450 people, including 24 MPs, described the plan as "totally irresponsible and out of touch with reality" and concluded wolves and livestock cannot live together.
Farmers also object to the limits on how many wolves can be killed, fixed at 40 this year and 10 percent of the total population thereafter.
Farmers can shoot wolves if their flocks are attacked at any time by culls are only allowed in clearly defined areas where there have been a number of attacks between 1 September and 31 December.
For all the opposition from the wolves' enemies, the plan has also drawn criticism from their friends.
"Once again the wolf is a victim of a lack of political courage," a statement by four NGOs declared.
The government "is continuing to treat the wolf as a pest" and threatening its long-term survival by authorising shooting without proof that it is effective, animal protection group Asppas said.
Admitting that scientific knowledge of the animal is limited, the plan proposes new studies should be carried out to find out how effective culls are, what its effects on the ecosystems are and to look into interbreeding with dogs.