France imposes 6:00 pm nationwide virus curfew
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The measure will remain in force for at least two weeks, Castex told a news conference.
Except for emergency services, all services and shops will have to close at that time, he said.
"The virus is still spreading actively," Castex said.
Up to now, most of France has been under an 8:00 pm curfew, with some parts of the country, especially in the hard-hit east, already under the stricter 6:00 pm curfew that Castex said had resulted in an infection rate two or three times lower than in the rest of the country.
Castex said a much-feared infection surge following the year-end holidays had not happened "thanks to your behaviour," but said a new lockdown could be imposed "without delay" if the health situation were to deteriorate badly.
The situation in France is "under control compared to neighbouring countries but still fragile," he warned, with pressure on hospitals still "high but stable."
Schools will remain open, but indoor sports activities have again been banned for now.
First-year university students will be authorised to return to their courses on-site, but with reduced numbers of participants, from January 25.
Castex also said that travellers arriving in France from non-European Union destinations would have to present a negative PCR Covid test less than 72 hours old, and would have to self-isolate for seven days. They would then have to take a second PCR test.
The new measures were partly motivated by fears that new mutant variants of the virus, first found in Britain and South Africa, would become a dominant spread factor, Castex said.
For now, the new strains represent 1 to 1.5 percent of new contaminations.
To speed up a vaccination drive that critics have slammed as too slow compared to France's European neighbours, Castex said people with illnesses making them particularly vulnerable to Covid will have access to vaccinations starting Monday, when "more than 700" vaccination centres would be operational.
He added that over one million people will have been vaccinated by the end of January, in line with targets announced in late December.
Castex also defended the decision to prioritise vaccines for the elderly and health workers, instead of trying to vaccinate as much of the general population as soon as possible.
"The sooner we can vaccinate the most vulnerable, the sooner our hospitals will be spared the risk of being overwhelmed," he said.