Lucas Hernández whipped a cross in from the left, and Griezmann sent a looping header back up over Manuel Neuer into the far corner.
The 27-year-old forward cancelled out Toni Kroos' first half penalty with a fine header just past the hour and then scored with a spot-kick himself late in the game to kill off the visitors' hopes of reaching the semi-finals.
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.
The result in Paris means they have now suffered six defeats in a calendar year for the first time and, following Saturday's 3-0 humbling reversal in the Netherlands, have lost two consecutive competitive matches for the first time since 2000.
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. "We were unable to put the ball in the goal", said Loew.
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"We had to stay alert at the back. stay calm and composed so as not to concede the second goal".
Griezmann stepped up to take the effort from 12 yards, with the Atletico Madrid attacker successfully sending Neuer the wrong way for his 26th goal for his country.
"But the penalty was totally unjustified".
The French found themselves on the backfoot in the first half but did not lose confidence even when the Germans came close to a second goal. I just watched the replay. Mats didn't touch Matuidi. "When you are not having a good day, you can change the system and the players, but (the French team) never gives up, and that's how we keep going".
"It's a good thing in terms of our aim of finishing top of the group but we were up against a very good German side today", said Deschamps.
It was a sixth defeat in the past 10 games for Löw's squad, who crashed out of the group stages at the World Cup in Russian Federation and remain bottom of their Nations League table with just one point from three matches.