Health Minister Olivier Veran warned earlier the situation was risky and said infections were essentially happening among 20 to 40 year-olds at parties.
Cases among older people were starting to rise too, Veran said, but he ruled out another total lockdown in France.
Sunday’s health ministry figures showed the number of people in hospital edged down by two to 4709 from the previous day, however.
Three more people were registered in intensive care, taking that total to 383.
Total coronavirus deaths rose by one in the past 24 hours to 30,513.
The country has recorded a total of 242,899 infections.
In Italy, Sicily’s governor ordered all migrant residences to shut down by Monday, part of a push-back by Italian regions alarmed by a surge in COVID-19 cases a few weeks before schools reopen.
But while some new migrants have tested positive, vacationers returning from Mediterranean Sea resorts abroad as well from the Italian island of Sardinia have accounted for far more of Italy’s new infections.
On Saturday, Italy registered 1071 new cases, the highest daily number since mid-May and only weeks after the nation had seen the number of day-to-day new infections plunge to about 200.
The Lazio region, which includes Rome, surpassed hard-hit Lombardy on Saturday for the highest daily new caseload, as returning travellers got tested at Rome-area airports and a port north of the Italian capital.
On the mainland, most of the latest cases were linked to travellers coming from abroad.
Those arriving from Spain, Malta, Greece and Croatia must be tested within 48 hours of entering Italy, after those places started experiencing worrisome upticks in coronavirus infections.
And many recent clusters have been traced to people who vacationed on Sardinia.
With many people taking ferries from Sardinia to the Italian mainland, Lazio set up a testing facility at Civitavecchia’s dock, so those driving vehicles off the boats could line up for immediate testing.
Lazio Governor Nicola Zingaretti appealed to the governor of Sardinia to test vacationers before they sail or fly from the island to the mainland, saying his region would do the same for travellers leaving for Sardinia.
In Sicily, Governor Nello Musumeci’s ordinance took effect on Sunday, requiring all migrants who reach the island by sea be transferred off as part of measures to combat the spread of COVID-19.
It stipulates that all centres housing migrants awaiting processing of asylum applications be shut down by the end of Monday.
His order, effective through September 10, also forbids any boat, including charity vessels, to bring migrants to the island.
On Saturday, migrants accounted for 16 of Sicily’s 48 confirmed infections.
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