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.
Nepal flood death toll crosses 1,000, rescuers reach remote areas
The death toll from Nepal's devastating floods surpassed 1,000 on Tuesday as rescuers deployed heavy machinery, helicopters and excavators to reach thousands still missing nearly a week after the Himalayan disaster tore through towns and valleys.
UK former PM Starmer quits parliament to focus on international affairs
Keir Starmer will stand down as a member of parliament, he said on Tuesday, some six weeks after he resigned as Britain's prime minister having lost the support of his Labour Party.
Novartis pauses trials of experimental cell therapy after three deaths
Novartis said on Tuesday it paused eight clinical trials of an experimental cell therapy, called rap-cel, targeting autoimmune and neurological disorders in late August, after three patients died.
Israeli strikes kill four in Gaza as military says it arrests Hamas fighter
An Israeli-backed raid to detain a Hamas official in Gaza City was discovered during the operation on Tuesday, prompting airstrikes to cover their withdrawal that killed at least three Palestinians, Gaza officials said.
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