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.
Russian attack on Kyiv kills three, injures 31
Ukraine's President Volodymyr Zelenskyy called for new strong sanctions against Russia and its allies after Russian drones killed three and injured 31, including six children, in an overnight air attack on Kyiv.
Israeli military says it conducted 'targeted strike' in central Gaza
Israeli forces carried out a "targeted strike" on an individual in central Gaza who was planning to attack Israeli troops, Israel's military said on Saturday.
Trump oversees Thailand-Cambodia ceasefire agreement
The leaders of Thailand and Cambodia signed an enhanced ceasefire deal on Sunday in the presence of US President Donald Trump, who intervened in July to bring an end to their deadly five-day border conflict.
Thailand's Queen Mother Sirikit dies at 93
Thailand's Queen Mother Sirikit, who brought glamour and elegance to a postwar revival in the country's monarchy and in later years, would occasionally wade into politics, has passed away at the age of 93, the Thai Royal Household Bureau said on Saturday.
Louvre transfers jewels to Bank of France after heist
The Louvre has transferred some of its most precious jewels to the Bank of France, according to French radio RTL, after an audacious daylight heist last week exposed the famed museum's security vulnerability.
