On Thursday 34,998 new cases of COVID-19 were reported, which actually marked a reduction from Wednesday's 38,000 new cases.
France was one of many European countries that had suspended the rollout of the Oxford/AstraZeneca vaccine earlier this week, citing concerns over reports of people developing blood clots after the jab.
The progression of the Covid-19 epidemic in France is clearly accelerating, Castex said.
According to Castex, who spoke during a news conference, the measures will come into effect on Friday from 7pm.
The French prime minister said there were increased threats due to a "third wave" with almost 1,200 people in intensive care in the Paris region even as the British variant of the virus has been responsible for the most number of cases in recent weeks.
However, the new measures will not be as strict as the previous lockdown, with people allowed to exercise outdoors within six miles of their home.
The lockdowns will kick in from Friday at midnight in France' 16 hardest-hit departments that, with the exception of one on the Mediterranean, form a corridor from the northern Channel port city of Calais to the capital.
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Schools will remain open.
Residents in affected regions will not be allowed to travel to other areas, except for essential business, said Castex.
Outdoor activity will however be curbed as the French PM warned, "go outdoors, but not to party with friends".
Meanwhile, a curfew that has been in place nationwide will also relaxed all over France so it ends at 7:00 pm rather than 6:00 pm to take account of the longer days, Castex said.
France recorded its highest daily number of coronavirus cases in almost four months on Wednesday, with the hard-hit Paris region bracing itself for a possible weekend lockdown to stem the rising tide of cases.
Castex, 55, said that as a person of his age with no underlying health conditions he had been ready to wait his turn until later in the year for a vaccination, but had changed his mind to help restore confidence in AstraZeneca's shot.
Not everyone agrees. In the intensive care unit of a private hospital on the edge of Paris, doctors expressed resignation at having once again to deal with overloaded wards.