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.


Belarus frees Nobel winner, protest figures as US lifts more sanctions
Indonesia flood death toll exceeds 1,000
Ukraine's Odesa suffers major blackouts after Russian attack
Two killed in Ukrainian drone strike on Russia's Saratov
Thailand continues Cambodia strikes despite Trump's ceasefire claim
