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 allies rebuff Trump's request for support in Strait of Hormuz
Several U.S. allies said on Monday they had no immediate plans to send ships to unblock the Strait of Hormuz, rebuffing a request by President Donald Trump for military support to keep the vital waterway open.
Pakistan-bound oil tanker passes through Hormuz Strait amid Iran war
Ship-tracking data shows a Pakistan-bound oil tanker passing through the Strait of Hormuz over the weekend, indicating that some countries are able to negotiate safe passage for their vessels despite the US-Israeli conflict with Iran.
Iranian women's soccer team begin journey home after players decline asylum
The Iranian women's soccer team began making their way home from Malaysia on Monday, after five of its players withdrew their claims for asylum in Australia.
Israel says it has plans for at least three weeks of war as airstrikes pound Iran
Israel said on Monday it has detailed plans for at least three more weeks of war as its military countinued to pound sites across Iran.
WHO says six hospitals evacuated in Iran, system holding up
A World Health Organization official said on Monday that the U.S.-Israeli war on Iran has led to the evacuation of six hospitals but that so far the system appeared to be holding up and authorities have not sought emergency relief from the global health agency.
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