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.
Drone, missile attack on Kyiv injures 26, damages buildings
Russian forces launched a massive drone and missile attack on Kyiv early on Friday, striking residential buildings and triggering explosions and fires across the Ukrainian capital, officials said.
BBC apologises to Trump over speech edit but rejects defamation claim
The British Broadcasting Corporation sent a personal apology to US President Donald Trump on Thursday but said there was no legal basis for him to sue the public broadcaster over a documentary his lawyers called defamatory.
Indian Prime Minister Modi's alliance set to easily win Bihar vote
Indian Prime Minister Narendra Modi's ruling coalition is set to comfortably retain power in state of Bihar, a vote count showed on Friday, giving him a boost after a disappointing national vote last year.
India's top court asks lawyers to argue online as air quality worsens
India's Supreme Court has asked lawyers to stay away and argue cases on a virtual platform instead, media said, in the latest disruption to life in the capital caused by deteriorating air quality.
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