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.
Israeli airforce pounds Beirut, Lebanon death toll rises
Israel pounded Beirut's southern suburbs with airstrikes on Friday, stepping up a war with Hezbollah that has forced hundreds of thousands of Lebanese from their homes and killed more than 200, according to a health ministry toll.
Hezbollah warns Israeli residents to evacuate towns near border
Lebanon's Hezbollah warned Israeli residents to evacuate towns within 5 km of the border between the countries in a message posted on its Telegram channel in Hebrew early on Friday.
US House rejects war powers resolution, backs Trump on Iran war
The US House of Representatives rejected an effort on Thursday to stop President Donald Trump's air war on Iran and require that any hostilities against Iran be authorized by Congress, backing the Republican president's military campaign.
Saudi Arabia, Qatar, Kuwait intercept drones targeting territory
Multiple Gulf countries, including Saudi Arabia, Qatar, and Kuwait, have announced their successful interception of several drones targeting their territories and airbases.
GCC and EU ministers urge immediate halt to Iranian attacks
Foreign ministers from the Gulf Cooperation Council (GCC) and the European Union have strongly condemned the Iranian attacks targeting GCC states, calling them a direct threat to regional and global security.
The UAE air defences said it has intercepted 9 ballistic missiles detected in the region on Friday. Of the 112 drones detected, 109 were intercepted with 3 falling within the country's territory.
His Highness Sheikh Mohammed bin Rashid Al Maktoum, Vice President and Prime Minister of the UAE and Ruler of Dubai, issued a new law on Friday, aimed at strengthening public safety across Dubai, setting out stricter standards for venues, events and public spaces.
UAE President His Highness Sheikh Mohamed bin Zayed Al Nahyan and Malaysian Prime Minister Anwar Ibrahim discussed, on Friday, the latest developments in the region and the escalating military action that threatens regional and international security and stability.
