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.
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Kuwait, Bahrain strongly condemn Iranian attack on ADNOC vessels
Kuwait and Bahrain on Saturday expressed their strong condemnation of the Iranian attack against vessels affiliated with the UAE's Abu Dhabi National Oil Company (ADNOC) while transiting the Strait of Hormuz.
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Morocco arrests 111 migrants headed for Spain's Ceuta in security crackdown
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