Borne was previously Minister of the Environment, Transport and Labour.
She will lead a French government likely to be tasked with delivering on President Macron’s election campaign priorities: pension reform and stepping up policies to tackle climate change.
Borne was “in charge of forming a government”, according to the Elysée.
She dedicated her appointment to “every little girl”, at a ceremony on Monday marking the handover.
“Follow your dreams to the end,” Borne said in a speech. “Nothing should hinder the fight for the place of women in society.”
Earlier Monday, the Elysée announced that Castex had tendered his resignation.
A former mayor of his small hometown of Prades in southwestern France, Castex was a little-known figure when he became prime minister in July 2020. He went on to lead France’s response to the Covid pandemic -19.
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