"When we look at three of the worst matches of my career, there are at least two before which I had a concussion a few days earlier," Varane told French sports daily L'Equipe.
Varane pointed to France's 1-0 quarter-final defeat to Germany at the 2014 World Cup and a 2-1 Champions League last-16 second leg loss while playing for Real Madrid in 2020 against Manchester City.
A few days before the Germany game, the defender said he took a ball to the side of the head during a last-16 match against Nigeria.
"At the start of the second half, there's a cross where I take the ball on one of my temples, and I run into the net of the opponent's goal. I finished the match but I was in 'autopilot' mode.
"The staff wondered if I was fit (for the Germany game)," continued Varane, who ended his international career after France were defeated in the final of the 2022 World Cup.
"I was weakened, but ultimately I played and rather well... What we'll never know is what would have happened if I had taken another knock to the head.
"When you know that repeated concussions potentially have a fatal effect, you tell yourself that it could go very wrong.
"As footballers used to playing at the highest level, we are accustomed to pain, we are a bit like soldiers, tough guys, symbols of physical strength, but these (concussions) are symptoms which are quite invisible.
"We need to talk about the dangers linked to second impact syndrome, and to the repetition of knocks because of head play," he added.
He called for a reduction in heading the ball during training sessions in order to reduce risks.
Second impact syndrome happens when the brain swells rapidly after a second concussion before symptoms from an earlier concussion have subsided.
In England, 10 former professional players and the families of seven others who have died are suing the governing bodies, which they claim have "always been perfectly aware" of the risks of concussions and brain injuries on players without taking the necessary precautions.
