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.
MS NOW, CNN and Politico to sue over White House ban
MS NOW, CNN and Politico said on Monday they were suing the Trump Administration to protect their First Amendment rights after President Donald Trump's announcement that he would ban the news outlets from the White House's building grounds.
Afghanistan says Pakistani airstrikes kill at least three
Pakistani airstrikes killed at least three people in Afghanistan on Monday, Afghan officials said, in action that could reignite tensions between the neighbours after nearly three months of relative calm.
New air traffic control failure delays flights at UK airports
Flights at several British airports were delayed on Monday due to an air traffic control failure, Britain's NATS air traffic control provider said, less than two weeks after a separate issue halted flights across the country.
Textile factory fire in southern Chinese city of Foshan kills 8
A fire that broke out at a textile factory in the Chinese city of Foshan in southern Guangdong province on Sunday killed eight people and injured one, state media said on Monday.
Typhoon approaches eastern Japan, prompts flood and landslide warnings
A powerful typhoon was approaching Japan's Pacific coast on Monday, bringing torrential rain, violent winds, and a heightened risk of landslides across the Kanto region and other parts of eastern Japan, the weather agency said.
6:00pm - 7:00pm
An extra hour of the UAE's biggest radio show for your drive home.
Ain't In La
Adéla
Save Your Tears
The Weeknd
Let Me Be
The Second Voice & Elvin Cena