The midfielder, who was operated in Gijon on a torn Achilles tendon in the right leg, sent a video to his teammates and fans.
"I wanted to send a message to all the fans for all the messages of support, thank you very much," Coquelin said in the video, after the players had taken the pitch with supportive t-shirts for him.
"You know that it was a very hard blow for me, a serious injury, but I saw the match against Alaves and it was very nice to see everyone chanting my name and, of course, with a great 3-1 victory.
"That is why I wanted to say thank you to all the fans, the club and the team for the support.
"I will come back stronger, let's go Valencia!"