It was a sixth defeat in the past 10 games for Löw's team, who crashed out at the group stage of the World Cup and remain bottom of Nations League Group A1 with one point from three matches.
Toni Kroos struck a 14th-minute penalty for Germany, but Griezmann engineered a rousing fightback in the first game between the nations at the Stade de France since the November 2015 friendly that was overshadowed by a series of terror attacks on the French capital.
Lucas Hernández whipped a cross in from the left, and Griezmann sent a looping header back up over Manuel Neuer into the far corner.
Yet without Griezmann making the difference on Tuesday, and the telling contribution of second-half substitute Kylian Mbappe against Iceland, France would have perhaps been faced with their first defeat since March.
After that defeat, Loew admitted there was a debate about whether he should still retain his job.
Thilo Kehrer nearly doubled the lead for Joachim Low's troops in the 24th minute with a brilliant header following a corner, but Les Bleus shot-stopper Hugo Lloris kept his team in the game with a good save.
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Antoine Griezmann got both of France's goals.
"We managed to win the World Cup thanks to our mental qualities, despite some hard moments", said Varane.
France now sit four points clear at the top of Group A1, while Germany are without a win in three games in this competition and can not qualify for the final stage.
"But the penalty was totally unjustified". The team played really well and attacked courageously. I just watched the replay. It was Matuidi who stepped on his foot and slipped, so this penalty was totally unfair.
Deschamps said: "This team has character, we have proved that already. I think we were disrupted by them playing three at the back, so we had to calmly speak a bit in the dressing and change two or three things tactically", Griezmann told French television.