The relatively low-profile Castex replaces Edouard Philippe, who resigned earlier in the day. Macron is reshuffling the government to focus on restarting the economy after months of lockdown.
As much of the world grapples to find the path forward, with the deadly virus still spreading in some places and a vaccine at best a distant reality, Europe is slowly emerging from isolation.
Larger shops and those in major German cities will open later as part of an attempted phased return to a more normal existence that will also see some students go back to school from May 4.
The number of coronavirus cases worldwide has passed 155,000, driven by a spike in infections in Italy, which announced 3,497 new cases on Saturday. The virus has so far claimed almost 6,000 lives across 154 countries and territories.
France is stepping up its effort to contain the virus, but the precautions shut the doors of some of the top tourism landmarks in the country, including the Eiffel Tower, the Louvre museum, and Paris' famed Moulin Rouge cabaret.
Prime Minister Edouard Philippe has said he would drop plans to increase the official retirement age to 64 from 62 in an effort to end a strike which has paralysed Paris and its suburbs, with bus, train and metro services all badly disrupted.
The challenge thrown to President Macron over his plans for radical pension reform has seen hundreds of thousands take to the streets and key transport services brought to a standstill.
Transport workers went on strike over the French government's plan to reduce retirement privileges as part of President Emmanuel Macron's pension reform plans.
While a host of French billionaires and companies offered donations worth around $1 billion, President Emmanuel Macron made a difficult promise – that the cathedral will be rebuilt within five years.
Paris will introduce legislation in February to toughen sanctions on undeclared protests in response to violent yellow-vest demonstrations.
Three opposition parties, the Socialist Party, far-left Defiant France and the Communist Party are setting aside their divisions and promise to submit a request to seek a no-confidence vote in the lower house of parliament.
President Emmanuel Macron is also set to address the country later in the day as he seeks to placate "yellow vest" anti-government protesters who wreaked havoc in Paris this weekend.
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