It's after the resignation of Edouard Philippe who has been in the post for three years.
Mr Castex, 55, is relatively unknown in France, although he is a senior civil servant.
The new Prime Minister has been a key player in the government's response to the Covid-19 pandemic.
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Russian drones injure 20 in Ukraine's Kharkiv, Dnipro
Russian drones attacked Ukraine's second-largest city, Kharkiv, and the southeastern city of Dnipro late on Monday and overnight, injuring more than 20 people, Ukrainian officials said.
Trump says war could be over soon, as Iran rallies behind new leader
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Saudi Arabia, Jordan condemn attack on UAE consulate in Iraqi Kurdistan
Saudi Arabia and Jordan have strongly condemned the recent attack targeting the UAE Consulate General in the Kurdistan Region of Iraq.
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