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.
Trump vows to blockade Strait of Hormuz after Iran peace talks stumble
President Donald Trump said on Sunday the US Navy would immediately start blockading the Strait of Hormuz, raising the stakes after marathon talks with Iran failed to reach a deal to end the war, jeopardising a fragile two-week ceasefire.
Nigerian airstrike hits market, 200 feared dead
At least 200 people are feared dead after Nigerian military jets struck a village market while pursuing rebels in the northeast of the country on Saturday night, a councillor for the area and residents said on Sunday.
Russia, Ukraine trade accusations of ceasefire violations
Russia and Ukraine accused each other on Sunday of breaching the 32-hour ceasefire in their four-year war, reporting more than a thousand drone and shelling attacks just hours after the truce began on Saturday to mark Orthodox Easter.
At least 30 dead in stampede at Haiti’s historic Laferriere Citadel
At least 30 people were killed on Saturday in a stampede at the Laferriere Citadel in the northern countryside of Haiti, authorities said, warning that the death toll could rise.
Cyclone lashes New Zealand's North Island, hundreds evacuated
A cyclone battered New Zealand's North Island on Sunday, cutting power to thousands of residents and forcing hundreds to evacuate, as officials warned conditions would worsen through the day.
