Officials are tightening measures to curb the spread but are reluctant to resort to the sweeping closures imposed during the initial peak of the pandemic in March and April.
France reported 3,602 new Covid-19 cases over the past 24 hours as infections climb across Europe.
While Saturday's (Aug 22) figure was lower than the 4,586 new cases the government's health office reported on Friday and the four-month record the previous day, the number is still above levels since May.
Meanwhile, Italy emerged as an unlikely role model for its handling of the pandemic, after suffering one of Europe's earliest and fiercest outbreaks.
Italy recorded 1,071 cases on Saturday, the most since mid-May but still well below the new peaks recorded in France and Spain.
In France, President Emmanuel Macron said this week that the damage from another national lockdown would be too high, and the country will have to rely on targeted local restrictions.
The nationwide lockdown earlier this year stifled the virus but sent the economy into its worst tailspin on record.
France requires masks to be worn in busy outdoor areas of cities such as Paris and Marseilles, while Toulouse began to mandate mask-wearing throughout the city on Friday. Face coverings will also become the norm in most indoor work areas starting in September.
Despite the rising case numbers, fatalities remain well below those earlier this year. Deaths increased by nine to 30,512 in the past 24 hours.
In Italy, the intensity and duration of its lockdown is widely seen as one of the reasons why cases did not pick up quickly after curbs started to be gradually lifted in early May, but rather kept falling.
Restrictions were maintained for a full six weeks after new infections peaked, and schools never reopened unlike in France or Germany.
Paradoxically, the fact that Italy was hit first - and hard - by the pandemic strengthened its response. Images such as those of army trucks loaded with coffins in the northern city of Bergamo started circulating at the height of the infection in March, and played a role in driving home the gravity of the situation.
Rules prescribing the use of faces masks are, somewhat uncommonly for Italy, largely respected. It is normal to see people wearing them in the streets, while indoors, in shops and offices, they are almost ubiquitous.
The relative success was due to "the strict lockdown, the use of masks and the increasing testing until July", said University of Milano-Bicocca virologist Francesco Broccolo. "Italians are now used to being more careful and there could be fewer people susceptible to the infection because of an immunity."
Yet, those accomplishments now at risk, and Italy is experiencing a resurgence in cases just like the rest of Europe.
The government has acted to stem the contagion, becoming one of the first European countries to require tests for arrivals from popular destinations like Greece and Spain. It then went further by closing down nightclubs and requiring face masks to be worn after 6pm in public gathering areas.
"We can't waste all the sacrifices we've made in past months," Health Minister Roberto Speranza said in a Facebook post on Aug 17. "The numbers of the infection in Italy, even though among the lowest in Europe, are rising."
As tourists keep coming back in August, cases could rise further, Professor Broccolo said, especially as some regions have been slow to set up testing at airports.
Almost a third of Italian new cases in the week to Aug 16 were imported from abroad, the National Health Institute said. The ratio climbs to almost half in the Milan area, especially arrivals from Croatia, Malta, Spain and Greece, Lombardy Health Secretary Giulio Gallera said on Aug 18.
The fact that most of the infected are asymptomatic and that the median age of new cases is 30 further complicates things.
In recent days, Italy has stepped up testing and tracing. Daily tests are now at levels last seen in early June, while the positivity rate remains low - less than 1.5 per cent, compared with more than 3 per cent for France and Spain.
Domestic transmission remains an issue, though. About 30 per cent of cases in the Lazio region around Rome are now linked to arrivals from the Italian island of Sardinia, prompting the government to consider some travel restrictions.
"I'm optimistic that a new lockdown won't be needed," said Prof Broccolo. "But to avoid that we need to do more tests. And we had to do it earlier, with quick testing. And never lower the guard. We were becoming too complacent."