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.
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".
New Lebanon-Israel talks begin in shadow of US-Iran deal
Lebanon and Israel began a new round of talks on Tuesday in Washington, with Beirut determined to press ahead with direct negotiations even as they appear to be overshadowed by Iran's decision to make Lebanon part of its talks with the US.
EU hosts Taliban officials in Brussels for first time
A delegation from Afghanistan's Taliban met on Tuesday with EU officials in Brussels for the first time.
