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 imposes sanctions on International Criminal Court
US President Donald Trump's administration has imposed sanctions on the International Criminal Court on Friday, hours after one of its former judges won the Nobel Peace Prize, putting Washington on a diplomatic collision course with European allies.
Three Saudi nationals killed in attacks on Riyadh airport, aviation authority says
Saudi Arabia's civil aviation authority said on Friday that three Saudi nationals were killed and several people were injured in two attacks on King Khalid International Airport in Riyadh on Thursday.
Former ICC judge Navi Pillay wins 2026 Nobel Peace Prize
Navi Pillay, a former ICC judge who oversaw a UN report that concluded Israel committed genocide in Gaza, won the Nobel Peace Prize on Friday "for her efforts to promote peace and international law".
Renoir paintings stolen from Riviera museum recovered, 6 people arrested
Two Renoir paintings worth millions of dollars that were stolen from a museum on the French Riviera a month ago have been recovered, and six suspects have been arrested, the local mayor said on Friday.
Hurricane Isaias strengthens as it heads for US Gulf Coast
Hurricane Isaias is strengthening as it heads for the US Gulf Coast, prompting evacuations in Florida and shutting in more than half of the coast's oil production.
UAE Attorney-General Dr. Hamad Saif Al Shamsi said investigations into the flydubai flight FZ1073 revealed the co-pilot began a "premeditated terrorist plot" to seize control of the aircraft and use it to launch an "suicide attack" targeting the passenger terminal at Ben Gurion Airport in Tel Aviv.
Etihad Airways and flydubai have announced cancellations of flights to Saudi Arabia's capital city of Riyadh for two days after Houthi missile attacks targetted King Khalid International Airport.
The UAE's National Media Authority has taken legal action against an individual who posted social media content that included the bullying of a child with disabilities.
