A study led by the Pasteur Institute has found that just 4.4% of the French population - or 2.8 million people - have been infected by the novel coronavirus, much higher than the official count of cases but too low to achieve so-called "herd immunity".
In a study published in the journal Science, researchers say the infection rate in the worst-hit parts of France - the eastern part of the country and the Paris region - is between 9% and 10% on average.
"Around 65% of the population should be immune if we want to control the pandemic by the sole means of immunity", the study says.
Herd immunity refers to a situation where enough people in a population have immunity to an infection to be able to effectively stop that disease from spreading.
The rate of infection was measured by the Pasteur Institute as of 11 May, the day when France started to unwind its almost two-month-long national lockdown.
"As of a consequence, our results show that, without a vaccine, the herd immunity alone will not be enough to avoid a second wave at the end of the lockdown. Efficient control measures must thus be upheld after 11 May, researchers say.
France's overall death toll from the virus rose to 27,074 yesterday, the fifth-highest in the world, and total number of cases officially stood at 177,700, the seventh-highest total.
The Pasteur Institute also said the lockdown put in place on 17 March in France led to a drastic decline of the coronavirus' reproduction rate, going from 2.9 to 0.67 over the 55-day virtual standstill of the country.
A Spanish study also published yesterday showed similar results, saying about 5% of the country's population had contracted the disease and that there was no herd immunity in Spain.
Meanwhile, the French government cried foul today after its homegrown pharmaceutical giant Sanofi said it would reserve first shipments of any Covid-19 vaccine for the United States, slamming the move as "unacceptable".
Sanofi's chief executive Paul Hudson sparked the controversy after announcing that US patients would get first choice because their government was helping to fund the vaccine search.
"The US government has the right to the largest pre-order because it's invested in taking the risk," Hudson, a British citizen who took over last year, told Bloomberg News.
"That's how it will be because they've invested to try and protect their population, to restart their economy," he said. "I've been campaigning in Europe to say the US will get vaccines first."
His comments drew outrage from officials and health experts, who noted that the Paris-based multinational has benefited from tens of millions of euros in research credits from the French state in recent years.
"For us, it would be unacceptable for there to be privileged access to such and such a country for financial reasons," France's deputy finance minister Agnes Pannier-Runacher told Sud Radio Thursday.
Sanofi's chief in France, Olivier Bogillot, sought to play down his boss's comments on Thursday, saying "the goal is to have this vaccine available to the US as well as France and Europe at the same time".
But that would only be possible "if Europeans work as quickly as the Americans," Bogillot told BFM television, saying the US government had pledged to spend "several hundreds of millions of euros".
"The Americans have been effective in this period. The EU must be just as effective in helping us make this vaccine available quickly," he said.
In April, Sanofi joined forces with Britain's GlaxoSmithKline to work on a vaccine, though trials have not yet started, and any successful treatment would be available toward the end of next year at the earliest.
The row came as world leaders past and present have insisted that any eventual vaccines and treatments should be made available to everyone, free of charge.
Former President of Ireland Mary McAleese, South African President Cyril Ramaphosa and Pakistani Prime Minister Imran Khan were among more than 140 signatories of a letter saying any vaccine should not be patented while the science should be shared between nations.
The World Health Assembly, the policy-setting body of the UN's World Health Organization, holds its annual general meeting next week.
The signatories called on the WHA to rally behind the cause.
"Governments and international partners must unite around a global guarantee which ensures that, when a safe and effective vaccine is developed, it is produced rapidly at scale and made available for all people, in all countries, free of charge," the letter said.
"The same applies for all treatments, diagnostics, and other technologies for Covid-19."