Cavani scored both goals in the 2-1 victory over Portugal last Saturday, having netted 10 times in 15 appearances in qualifying to send Uruguay to Russian Federation.
The match at Nizhny Novgorod Stadium pitted France's speed against Uruguay's stubborn defence and its occasional attacking threats.
ARAB NEWS PREDICTS: France to win 2-1 - A lot depends on France coach Didier Deschamps, but if he allows his team to play then we can only see a France win, not least if Uruguay's injured striker Edinson Cavani cannot play. "In the World Cup, it is a different mentality", he said.
This is Russia's best World Cup run since the break-up of the Soviet Union.
Les Bleus' victory takes them to their sixth World Cup semi-final where they will meet Roberto Martinez's Belgium side.
Uruguay were semifinalists in 2010 but their campaign in Russian Federation marked just the second time after 1970 that they had advanced to the quarterfinals, and Godin wanted their achievment recognised. "He does not know the dedication we have to succeed in football with the few numbers we have".More news: Deadly Klamathon Fire Grows to 8,000 Acres in Northern California
Uruguay's defender Diego Godin celebrates their win during the Russian Federation 2018 World Cup round of 16 football match between Uruguay and Portugal at the Fisht Stadium in Sochi on June 30, 2018.
A relatively quiet game burst into life in the 40th minute when Varane sprinted clear of his marker to meet a well-placed Griezmann free kick with a perfectly angled header. "He's an important player, but France isn't just one player".
The Paris Saint-Germain hitman bagged a scintillating brace as Oscar Tabarez side displayed their usual defensive solidity with Cavani and Luis Suarez combining well up-front. France beat us and they beat us well.
"We've not got a good record against them, I think we've always underestimated them", he said.
"Speaking to Cadena COPE following Uruguay's triumph over Cristiano Ronaldo's Portugal, Suarez said", As a friend of Leo, and putting myself in his skin, it's been a very complicated day. "Apart from that, they didn't have many great opportunities".
Stuani replaced Cavani after he sustained the injury against Portugal in the second half of the game.