The atmosphere was unusually subdued when the race started in Nice on Saturday, fearing that the 176 riders would make it to the finish line in Paris.
The president of the International Cycling Union, David Lappartient, said it was “a first miracle that we could start this race”.
“But we want a second miracle to happen, namely that the Tour de France arrives in Paris,” he added.
French Sports Minister Jean-Michel Blanquer took on a more optimistic tone, saying that if “anything is possible” the chances of the Tour being canceled before arriving in Paris were “very slim”.
France is facing a steadily rising infection rate, with a post-lockdown high of 7,379 new cases recorded on Friday.
In light of the resurgence, health authorities imposed stricter restriction rules on the race hours before it started.
The new rules state that an entire team – consisting of eight runners and 22 staff – will be expelled from the race if two or more members test positive for COVID-19 within a week.
This rule previously only applied to runners.
Given that four members of the Lotto Soudal squad were sent home on Thursday after a mechanic and a goalkeeper tested positive, the change will reduce the peloton’s chances of reaching the Champs-Elysées in three weeks.
The Lotto Soudal team remained in the race as the changes were not adopted until Saturday.
Since its inception in 1903, the race has only been canceled during the two world wars. But organizers have admitted there is a risk it will not reach Paris as coronavirus cases continue to rise.
France’s health ministry said the country was seeing an “exponential” spread of cases, although there has not been a similar increase in hospitalizations and deaths.
President Emmanuel Macron has raised the possibility of another nationwide lockdown – days before 12 million children return to school.
Like other hard-hit Western European countries, France imposed a sudden and strict lockdown in March.
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These were gradually lifted from May 11 after infections fell sharply, and Mr Macron said he was “doing everything to avoid another lockdown”.
On Friday, the wearing of masks outdoors was made compulsory in Paris.
Some 267,000 coronavirus cases and 30,596 disease-related deaths have been recorded across the country.