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.
Palestinian teen shot dead in Israeli West Bank raid, Wafa reports
A Palestinian teen has been shot dead during an Israeli military raid in the occupied West Bank on Wednesday, the official Palestinian news agency Wafa reported.
Libya says 17 migrants perish at sea, nine missing feared dead
At least 17 migrants have died, and nine are missing after their boat broke down and drifted for eight days in the Mediterranean Sea, Libya's Red Crescent and Libyan security sources said on Wednesday.
Israel begins intercepting Gaza aid ships far from shores, army radio says
Israel has begun taking control of aid ships bound for Gaza far from Israeli shores, Israeli army radio cited an Israeli source as saying on Wednesday.
Trump urges Iran to sign a deal and discusses prolonged blockade
Donald Trump discussed how to mitigate the impact of a possible months-long US blockade of Iran's ports with US oil companies, a White House official said on Wednesday, as the US president urged Tehran to 'get smart soon' and sign a deal.
Seven people die in hospital wall collapse in southern India
Seven people have died after a 2.5 metre wall at a hospital complex collapsed in the southern Indian city of Bengaluru, a state official said on Wednesday.
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