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, Iran at odds on nuclear inspections, frozen assets in deal to end war
US President Donald Trump has stated on Tuesday that Iran had agreed to nuclear inspections into "infinity," while Tehran said it had made no such concession in negotiations, raising questions about the viability of their fragile peace deal.
Oman establishes temporary shipping corridor through Strait of Hormuz
Oman has coordinated with the International Maritime Organisation (IMO) to establish a temporary maritime corridor for vessels transiting the Strait of Hormuz, according to its local news agency.
Power cuts in France leave thousands sweltering amid scorching heatwave
Authorities in northern France were scrambling on Wednesday to restore electricity to thousands of homes hit by power cuts amid a blistering heatwave that has scorched much of western Europe for days.
Libya's eastern government bans entry of nationals from four African countries
Libya’s eastern-based government has banned the entry of nationals of four African countries on Tuesday, a decision a government source said was due to a "reorganisation of foreign nationals’ entry to Libya".
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