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.
AI leaders warn UN of security risks as systems grow more powerful
Executives from three of the world's leading artificial intelligence companies briefed the UN Security Council on Wednesday amid warnings that increasingly powerful AI systems could soon improve themselves, slip beyond human control and pose a threat to international security.
Rubio says Russia and Ukraine voiced interest in 'limited ceasefire'
Ukraine and Russia have both voiced an interest in a limited ceasefire involving grain and energy-related targets, US Secretary of State Marco Rubio said on Wednesday after meeting Russian Foreign Minister Sergei Lavrov in New York.
One killed in attack on ship off Oman coast while heading to India
One Indian national was killed in an attack on the bulk carrier MV Cape Dao while the vessel was heading towards India, the Indian embassy in Oman said on Wednesday.
Italy's Colosseum closes after worker dies in accident
Italy's Culture Minister Alessandro Giuli ordered the closure of the Colosseum to be extended until Thursday as a mark of respect after a worker was killed overnight in an accident.
Hope for progress after US, Iran hold first shuttle talks in months
The first shuttle talks between the US and Iran for months raised hopes on Wednesday that the adversaries could make some progress towards ending the Middle East war, although neither side spelled out any change in their positions.
