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.
Peace deal hopes fade after Trump rejects Iran proposal
Hopes for a peace deal on Iran faded on Tuesday after Donald Trump said a ceasefire with Iran was "on life support" as Tehran rejected a US proposal to end the conflict.
UK's Starmer defies calls to quit, says he is getting on with governing
Prime Minister Keir Starmer defied calls to resign on Tuesday, telling ministers he would "get on with governing" despite a "destabilising" 48 hours of growing calls to set out a timetable for his departure after an election drubbing.
New Israeli law sets military tribunal for those linked to October 7 attack
Israel's parliament passed a law late on Monday establishing a military tribunal to try hundreds of Palestinians who took part in the October 7, 2023, attack on Israel, a step lawmakers said would help heal national trauma.
Russia strikes Ukraine with drones as ceasefire ends
Russia launched more than 200 drones at Ukraine overnight, hours after a US-mediated ceasefire expired, dimming hopes it would be extended.
Dutch hospital quarantines 12 over breach of hantavirus protocol
A Dutch hospital quarantined 12 staff members in a preventive measure after blood and urine from a hantavirus patient were handled without observing strict protocols.
The UAE has strongly condemned the infiltration of Kuwait’s Bubiyan Island by members of Iran’s Islamic Revolutionary Guard Corps (IRGC) to carry out hostile acts.
Federal government employees in the UAE will get a week off to mark Eid Al Adha.
Dubai's private schools will get a nine-day break after Knowledge and Human Development Authority (KHDA) announced that Eid Al Adha holidays will begin on Monday, May 25, and end on Friday, May 29.
