The 27-year-old added to Raphael Varane's first-half header with a second just after the hour mark, effectively killing the contest, although the goal owed as much to a howler from goalkeeper Fernando Muslera as it did the quality of Griezmann's strike.
The Atletico Madrid man has spoken numerous times of his affection for Uruguay, having been handed his debut at Real Sociedad by mentor Martin Lasarte and worked alongside the likes of Diego Godin - the godfather to his daughter Mia - in the Spanish capital.
He said: "I didn't celebrate because when I started as a professional I was supported by a Uruguayan who taught me the good and the bad in football and I have a lot of respect for Uruguay.
"I was also playing against friends, so I thought it was normal not to celebrate.
"They're a tough team, like Atletico Madrid. Everyone works hard in attack and defence. It's something I see day in day out and I love Uruguayans and Uruguayan culture, so I have a lot of respect for them."
France ground out the win in a match high on energy but low on quality to set up a last-four clash with either Brazil or Belgium, who meet in Kazan.
Griezmann added: "We have a team who can hurt any defence. We have to continue working but when we focus on our style, we have a better chance of winning.
"We have people who know how to manage a game. I do something similar: when I have the ball, I try to take the game to where I want it to be."