Playing at Football Arena Munich, France had two goals disallowed for being offside coming from Kylian Mbappe in the 67th minute and Karim Benzema in the 84th.
Portugal also defeated Hungary 3-0, with the win taking them to the top of Group F above France on goal difference.
In a post-match press conference, French team manager Didier Deschamps said that his team played a flawless match against very good opponents.
"I knew my players would be ready and we were up for the fight," he said. "We weren't far away from scoring the second goal that would have made us safe, but we didn't suffer that much in the second half. It was a strong match with quality and talent."
Joachim Low, the German national team coach, said the match was an intense one that they fought until the very end, adding: "I cannot blame my team for not trying-they gave everything they had."
French star Paul Pogba said that they all put the effort in and they are all focused on their jobs on the pitch.
"We know we need to live up to our tag as world champions and come out onto the pitch with humility. When we need to suffer, we do it together and when we attack, we do it together," he said.
Sitting at a table to make the remarks, Pogba, a devout Muslim, removed a beer put there previously.
Before the game, a Greenpeace protester parachuted into Allianz Arena to protest oil consumption.
German automaker Volkswagen is among the sponsors of the EURO 2020.
The parachute bore the words "Kick out oil."
