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.
Afghan Taliban says 400 killed in Pakistan air strike on Kabul hospital
At least 400 people have been killed and 250 injured in an air strike by Pakistan on a drug users' rehabilitation hospital in Kabul, a spokesman of the Afghan Taliban government said on Tuesday, a sharp escalation in the conflict between the neighbours.
Bomb attacks kill at least 23 in Nigeria's Maiduguri
At least 23 people have been killed and 108 injured in suspected multiple bomb attacks in Maiduguri city, capital of Nigeria's insurgency-hit northeastern state of Borno, the state police command said in a statement late on Monday.
Five countries warn against major Israeli ground offensive in Lebanon
A "significant Israeli ground offensive" in Lebanon must be averted since it could have devastating humanitarian consequences, Canada, France, Germany, Italy, and Britain have said in a joint statement on Monday.
Fire breaks out at Qatar's industrial area after missile interception
Qatar's Ministry of Interior has announced that its civil defence forces are responding to a fire that broke out at its industrial area on Tuesday due to fallen shrapnel from a missile interception.
Kuwait arrests Hezbollah-linked cell in security crackdown
Kuwaiti security authorities have uncovered and arrested a cell linked to the banned organisation Hezbollah that was planning to destabilise the country and recruit new members.
