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.
Malaysia ex-PM Najib jailed for 15 more years in 1MDB case
Malaysia's former premier Najib Razak was jailed on Friday for a further 15 years and fined $2.8 billion for power abuse and money laundering in the biggest trial of the multibillion-dollar 1MDB scandal, a ruling that could have big political ramifications.
US launches strike against ISIS in northwest Nigeria
The United States has carried out a strike against IS targets in northwest Nigeria at the request of Nigeria's government, President Donald Trump and the US military said on Thursday, claiming the group had been targeting Christians in the region.
Israel formally recognises Somaliland as independent state
Israel became the first country to formally recognise the self-declared Republic of Somaliland as an independent and sovereign state on Friday - a decision that could reshape regional dynamics and test Somalia’s long standing opposition to its secession.
Explosion at mosque in Syria's Homs kills eight
Eight people were killed in an explosion at a mosque of the Alawite minority sect in the Syrian city of Homs on Friday.
Ukraine president discusses "bringing peace closer" with US negotiators
Ukrainian President Volodymyr Zelenskyy said on Thursday that he spoke with US President Donald Trump's special envoy Steve Witkoff and son-in-law Jared Kushner for about an hour on how to end the war with Russia.
