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.
Nine days after disaster, two pulled alive from Nepal hydropower tunnel
Two people were pulled out alive on Friday from a tunnel linked to a hydropower station on the Trishuli River in Nepal, nine days after an ice, rock and mud slide swept through its valley, killing more than 1,200 people and displacing tens of thousands.
Germany launches manhunt after spate of sabotage attacks on power grid
German police are searching for a man who sent letters claiming responsibility for a series of sabotage attacks on the power grid this week after they found what appeared to be explosives at his home, officials said on Friday.
Air India sack Phuket-Delhi pilot who failed drug test
The pilot-in-command of an Air India flight from Phuket to New Delhi that dropped nearly 300 feet last month, injuring several passengers, has been dismissed after testing positive for a psychoactive substance.
Wildfires spread near Indonesia's new capital, prompting calls for action
Wildfires have begun spreading near Indonesia's under-construction new capital, prompting project authorities to urge the disaster mitigation agency to carry out cloud-seeding and water-bombing operations, officials said.
Philippine court issues warrant for VP Duterte's arrest in grave threats case
A Philippine court on Friday ordered the arrest of Vice President Sara Duterte in connection with a criminal case accusing her of making threats against President Ferdinand Marcos Jr., the first lady, and a former House speaker.
1:00am - 3:00am
Cold Water
Major Lazer Ft. Justin Bieber & Mo
Mr Know It All
Teddy Swims