PARIS—The government of President Emmanuel Macron is preparing to cut the country’s unemployment benefits as the French leader seeks to reboot his economic overhauls and put months of violent yellow-vest protests behind him.

The government said Tuesday it planned to issue a decree in July capping the amount people can claim in unemployment benefits and extending the period people must work to qualify for the aid. The government will also increase payroll taxes on companies that use too many short-term contracts—a practice...