Goals from Thomas Muller and Leroy Sane at the start and end of the game gave Germany their first win in their last six matches and capped a turbulent few days for the four-time world champions.
While France, 2022 World Cup runners-up, did not field their strongest team, with captain and top striker Kylian Mbappe on the bench, Germany's overall performance was far improved from Saturday's 4-1 home loss to Japan that led to Flick's departure.
"For us, it was clear we'd be running a lot today," Muller said.
"It was a crazy situation in the past three days. But congratulations to Rudi and his staff on how they dealt with it.
"We did what we had to, we worked hard and we were rewarded for it. We should not read too much into this win but for us, it was a small emotional release."
The Germans, who had won four of their previous 17 matches before Tuesday, pressed high and were rewarded when veteran Muller rifled home from inside the box in the fourth minute for his 45th international goal after a fine 13-pass move.
The French gradually found their way into the game and grew more dangerous, with Randal Kolo Muani and Aurelien Tchouameni piling pressure on the home defence.
Tchouameni's low drive in the 57th forced a good save from Marc Andre ter Stegen, who also denied Antoine Griezmann in the 82nd by tipping his shot over the bar.
Sane then completed a quick break to score in the 87th before bringing down Marcus Thuram two minutes later for a penalty, with Griezmann cutting the deficit for the visitors.
