Addressing the National Assembly, Castex also said authorities would be quick to disperse groups of more than six people on riverbanks or squares after the new restrictions unveiled by President Emmanuel Macron late Wednesday.
Castex said he “unreservedly” condemned people who had not been respecting the rules, after images of beer-swigging crowds on riverbanks under spring sunshine in cities including Paris and Lyon.
Meanwhile, prosecutors should “systematically” probe organisers of clandestine parties for putting the lives of others in danger, he added.
By decreeing school closures and systematic work-from-home protocols, Macron hopes to ease pressure on hospitals facing a new surge in coronavirus cases that are overwhelming intensive care units.
But he refrained from demanding that people stay in their homes or avoid socialising completely, and authorised travel between regions over the coming Easter weekend.
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As during the first lockdown last spring, parents are scrambling to make arrangements for another round of distance learning with schools to close for three to four weeks.
Macron shuffled the timetable for school holidays and younger children will return to school on April 26th after taking their spring break, and older pupils will follow a week later.
Castex, who provided lawmakers with details of the new measures, said low-income families would receive financial aid for children no longer eating school lunches.
Health Minister Olivier Véran said the number of new Covid cases could peak in the next seven to ten days, while intensive care cases in hospitals might top out by the end of April.
“The goal is to suppress this wave of the epidemic… so that it’s as small as possible,” he told France Inter radio.