The two players were celebrating after setting up the first of France's two goals, which ultimately took them to a 2-1 victory over Germany.
Mathieu Debuchy, a midfielder with Lille, passed the ball to Montpellier player Olivier Giroud, who scored.
Debuchy then ran to Giroud who grabbed his head with both hands and kissed his teammate.
The video clip of the embrace was played repeatedly on news shows and shared online.
#Debuchy was still a trending Twitter tag on Thursday morning
The goal was Giroud's first for his national team. He is currently the top scorer this year in France's leading football league, Ligue 1.
Debuchy's team, Lille, are current Ligue 1 champions.
One of Debuchy's other team mates is former Chelsea and Liverpool player Joe Cole.
The 2-1 win for France brought the team's unbeaten run to 18 matches.
French team manager Laurent Blanc tried to play down the victory.
"The result didn't interest me. We only wanted to take a step forward," he said.
"It doesn't change anything about the work we need to do. The hardest thing is realising this quality of play in big tournaments. For quite a while, France has not been able to win those."