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.
Saudi coalition says it intercepts Houthi missiles, drones
Yemen's Saudi-led coalition said early on Saturday it had intercepted two ballistic missiles and two drones launched by the Houthis towards the kingdom.
Blast in Pakistan's Dera Ismail Khan kills 11, injures 30
Eleven people were killed and 30 injured in a blast in Dera Ismail Khan in northwestern Pakistan on Saturday, emergency service Rescue 1122 said.
Two dead, 4 missing after explosion destroys building in Athens
Two people have died and another four are missing after a residential building collapsed following an explosion in a tourist area of central Athens, a Greek fire brigade official said on Saturday.
TV networks resume covering White House as press access fight continues
US television networks resumed coverage of President Donald Trump’s White House events on Friday, providing the first live pool access for Chinese President Xi Jinping’s visit, as a legal battle continues over restrictions on CNN, MS NOW and Politico.
WHO says Congo Ebola outbreak spreads to two new health zones
The World Health Organization said on Friday that the Ebola outbreak caused by the Bundibugyo virus in the Democratic Republic of the Congo has spread to two additional health zones, bringing the total number affected to 63 across seven provinces.
