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.
South Korean ferry runs aground, all 267 people rescued
All 267 people on board a South Korean passenger ferry that ran aground off the southwestern tip of the Korean peninsula on Wednesday were rescued, in an incident that revived memories of the major ferry disaster in 2014 in which 300 people died.
Indonesia's Semeru volcano erupts, alert level raised to highest
Indonesia's Semeru volcano erupted on Wednesday and the country's volcanology agency increased the alert level of Java Island's tallest mountain to the highest.
19 killed and 66 wounded in heavy Russian attack on Ukraine
Nineteen people were killed in a heavy overnight Russian missile and drone attack that struck an apartment building in the western Ukrainian city of Ternopil, Ukrainian officials said on Wednesday.
Elon Musk, Ronaldo attend Trump's dinner for Saudi Crown Prince
Tesla CEO Elon Musk and Portugal's football star Cristiano Ronaldo were among the elite guests at a dinner hosted by US President Donald Trump for Saudi Crown Prince and Prime Minister Mohammed bin Salman bin Abdulaziz Al Saud at the White House.
Louvre museum to add 100 external cameras by 2026 after heist
France's Louvre Museum will install 100 external cameras by the end of 2026 as part of measures to tighten security after last month's spectacular heist, its director said on Wednesday.
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