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.
US seizes Russian-flagged oil tanker linked to Venezuela
The US seized a Russian-flagged oil tanker that was being shadowed by a Russian submarine on Wednesday, after pursuing it for more than two weeks across the Atlantic as part of Washington's efforts to block Venezuelan oil exports.
Power restored in Berlin after longest blackout since World War Two
Electricity was restored to southwestern Berlin on Wednesday after a suspected arson attack on a power station by leftist activists caused a blackout for tens of thousands of households, the longest outage in the German capital since World War Two.
France working with allies on plan should US move on Greenland
France is working with partners on a plan on how to respond should the US act on its threat to take over Greenland, a minister said on Wednesday, as Europe sought to address US President Donald Trump's ambitions in the region.
South Korea's Lee says he asked Xi to play a mediating role on North Korea
South Korean President Lee Jae Myung said on Wednesday that much progress had been made in restoring trust with Beijing, and that he had asked Chinese President Xi Jinping to play a role in mediating Seoul's efforts to engage North Korea.
Western Europe braces for another wave of snow and ice
Western Europe braced for more snow and ice on Wednesday, with the first named storm of the year hitting the continent's Atlantic coast.
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