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.
Five dead, dozens wounded as Russia launches major attack across Ukraine
Russian air attacks on major Ukrainian centres including Kyiv, Dnipro and Kharkiv have killed at least five people and wounded dozens early on Tuesday, authorities said, after days of warnings that Moscow was planning a major assault.
Trump says no Israeli troops will go to Beirut after call with Netanyahu
US President Donald Trump said on Monday that Israel would not send troops to Beirut after a call he held with Israeli Prime Minister Benjamin Netanyahu.
Moderna and other groups get $60 million to develop Ebola vaccine
Global health organisation CEPI will give roughly $60 million to Moderna and two other groups to accelerate the development of shots against Ebola Bundibugyo, the deadly virus that has swept through eastern Democratic Republic of Congo.
Bus driver charged with five counts of manslaughter in Virginia highway wreck
A tour bus driver has been charged with manslaughter stemming from the deaths of five people in a fiery chain-reaction crash that police say was triggered when the motor coach plowed into slower-moving traffic in a highway construction zone.
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