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.
Saudi-owned vessel targeted in Red Sea, crew safe, state news agency says
Saudi Arabian state news agency on Thursday confirmed that tanker Encelia was ablaze after an assault while sailing in the Red Sea.
Rubio says US committed to helping end Ukraine war after meeting Lavrov
US Secretary of State Marco Rubio said on Thursday that the United States remains prepared to play a "constructive role" in helping bring an end to the war in Ukraine, following talks with Russian Foreign Minister Sergei Lavrov on the sidelines of an ASEAN gathering in Manila.
India's Modi promises fast-track courts on exam leaks, protesters want minister to quit
Indian Prime Minister Narendra Modi said on Thursday that "fast-track" courts would be set up to prosecute those behind exam paper leaks, his first public response after days of youth protests demanding the resignation of the education minister.
Venezuela quakes caused $19.6 billion in damage, World Bank report shows
Two earthquakes that rocked Venezuela on June 24 caused $19.6 billion in direct physical damage, but the cost of rebuilding could be twice that much or more, the World Bank said in an early assessment released on Thursday.
Ousted Ukrainian defence chief digs in against Zelenskyy, protests grow
Ousted Ukrainian defence minister Mykhailo Fedorov said on Thursday he would accept no other government position besides his former job, escalating a political crisis that has gripped Ukraine at a pivotal point in the war with Russia.
