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The 33-year-old, who struggled at this year's Euros, was one of the key elements in the 2018 and 2022 World Cup campaigns as Les Bleus took the title in Russia and finished runners-up in Qatar.
Griezmann struck in each half after his partnership with Karim Benzema bore fruit in satisfying fashion to put the world champions on 12 points from six matches at the top of the group.
On Sunday night Griezmann and his teammates produced a pulsating performance before falling to the ground, hugging and sobbing as world champions.
Reactions after France beat Croatia 4-2 in the World Cup final on Sunday.
Barcelona goalkeeper Neto made an embarrassing gaffe as his side was held to a 1-1 draw away to Alaves, despite playing the final half an hour with an extra man.
The 28-year-old did not reveal where he would be playing next but widespread reports in the Spanish media said he would be joining Barcelona.
Griezmann's 120 million euros transfer was contested by Atletico, who insisted Barcelona should have paid a higher price for the World Cup-winning French striker.
France forward Griezmann, rejected a move to Barcelona last year but announced in May he was leaving the Madrid side, where he has spent the last five seasons since signing from Real Sociedad in 2014.
Messi returned from injury to make his second start of the season against Inter Milan in the Champions League as Barca came from behind to win 2-1 on Wednesday.
The victory takes Barcelona up to fourth with 10 points after six games, one point behind surprise leaders Granada, Athletic Bilbao, and Real Madrid.
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