Thomas Lemar gave France the lead on five minutes and Griezmann, who last month announced he was leaving Atletico Madrid after five seasons, notched a second before the break.
Griezmann moved eighth on the list of France's all-time leading scorers with his 29th goal as he surpassed 1998 World Cup winner Youri Djorkaeff.
Will Griezmann move to Barcelona this time around?
He is now just one goal behind Just Fontaine and Jean-Pierre Papin, and two adrift of Zinedine Zidane.
There was a slight note of concern for France though as they lost Kylian Mbappe to an ankle injury at half-time.
Didier Deschamps' side return to competitive action on June 8 when they face Turkey in Group H. Both nations have six points from two matches.
I’m leaving Atletico at end of the season: Griezmann
"We needed to get a little warm-up in. It's going to be tough in Turkey, we'll have to be ready," said Griezmann.
"I may not be in top form. This match will do me good, to get some minutes and be in good shape for Saturday."
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