Barnier, the EU's former Brexit negotiator, took office hours after Emmanuel Macron appointed him to form "a unifying government in the service of the country" - an attempt to put an end to two months of political paralysis after a snap election.
Barnier, who at 73 is the oldest prime minister in the history of modern France, said his first task was to "respond as best we can to the challenges, the anger, the feeling of abandonment and injustice that is too prevalent in our cities, on our estates and in the countryside".
The government's priority would be education, as well as security and controlling immigration, he said.
"What do we expect from a prime minister?" Barnier asked. "That they tell the truth, even if it's difficult the truth about debt, and the truth about environmental debt, which weighs heavy on the shoulders of our children." He said he would approach the role with "humility and determination" and promised "more action than words".
Macron shocked France by calling a snap parliamentary election in June, which resulted in a hung parliament and a deeply divided political landscape.
Although Marine Le Pen's far-right National Rally came top in the first round, tactical voting resulted in a leftwing coalition becoming the biggest political force in the final round.
But the left fell well short of an absolute majority of 289 seats in the national assembly.
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