Additional test were carried out on the Flying Fijians squad after a player - understood to be centre Semi Radradra - tested positive for the coronavirus on Tuesday.
Organisers of the Autumn Nations Cup made the decision to cancel the Test in Vannes on Friday after the squad returned the four new positive tests, which also affected a number of close contacts.
The match was scheduled to take place on Sunday local time but due to the tight schedule it was not possible to postpone the fixture to a later date.
"This was a difficult and disappointing decision, but it was the only possible outcome following today's test results," explained Ben Morel, CEO of tournament organisers Six Nations Rugby.
"Whilst we've all been eagerly awaiting this match, the welfare of our players and their support teams remain our number one priority.
In line with tournament protocols, the Fiji squad were being tested twice-weekly for Covid-19 in the lead-up to their opening fixture.
"We have a rigorous testing programme in place," Morel said.
"In this instance, it is impossible for the Fijians to field a competitive team and we have no other option but to cancel this match."
Tournament organisers said they were working closely with the Fiji Rugby Union to mitigate the impact of the outbreak and to ensure preparations can resume on time for Fiji's next match against Italy on 21 November.
Further rounds of Covid-19 testing will take place among the Fiji squad in the coming days, while the sporting outcome of the Fiji vs France match will be decided on Monday.