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 grants India six-month sanctions waiver to run Iran's Chabahar port
The US has granted India a six-month sanctions waiver to operate the Iranian port of Chabahar, India said on Thursday, boosting its efforts to enhance trade with Afghanistan and Central Asian countries bypassing Pakistan.
Trump cuts China tariffs to 47% after 'amazing' Xi meeting
US President Donald Trump said on Thursday he had agreed to reduce tariffs on China to 47 per cent in exchange for Beijing resuming US soybean purchases, keeping rare earths exports flowing and cracking down on the illicit trade of fentanyl.
Israel carries out new strikes in Gaza after asserting commitment to ceasefire
Israeli planes and tanks pounded areas in eastern Gaza on Thursday, Palestinian residents and witnesses said, a day after Israel said it remained committed to a US-backed ceasefire despite launching more lethal bombardments in the territory.
French police make more arrests in Louvre heist investigation
Police have arrested five more suspects linked to the theft of treasures worth $102 million from the Louvre museum's Apollo gallery, the Paris prosecutor said on Thursday, expressing hope the latest developments will help them find the jewels.
Afghanistan and Pakistan agree to restart peace talks in Istanbul, sources say
Afghanistan and Pakistan will restart peace talks in Istanbul, three sources familiar with the matter said on Thursday, a day after Islamabad said the discussions had ended in failure.
