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.
Iran vows to attack any ship trying to pass through Strait of Hormuz
An Iranian Revolutionary Guards senior official said on Monday that the Strait of Hormuz is closed and Iran will fire on any ship trying to pass, Iranian media reported.
Drones target fuel tanks at Oman’s Duqm Port
Several drones have targeted fuel tanks and struck one at Oman's Duqm commercial port on Tuesday, with no casualties reported.
At least 42 civilians killed in Afghanistan in conflict with Pakistan, UN agency says
At least 42 civilians have been killed and 104 wounded in Afghanistan in the fighting with Pakistan between February 26 and March 2, the United Nations Assistance Mission in Afghanistan (UNAMA)said on Tuesday, as the military conflict between the neighbours entered its sixth day.
Qatar announces interception of 2 jets, 101 missiles since Iranian attack
Qatar's Ministry of Defence has announced its successful interception of 2 SU-24 fighter jets, 98 ballistic missiles, 3 cruise missiles, and 24 drones since the start of the Iranian attack.
Two drones target US embassy in Saudi Arabia
Saudi Arabia's Ministry of Defence has announced that two drones targeted the US embassy in Riyadh on Tuesday.
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