Rami, who plies his trade for Marseille, has not played a single minute for his nation this summer but was among the celebrations as France won the tournament for the first time since 1998.
"The France team is over for me," Rami told reporters after the nation's triumph.
"Even if I did not play, I had to be ready at all times to play 90 minutes. I trained twice a day. The team was huge, I do not have words for that. The atmosphere is extraordinary."
Rami made his France debut in 2010 and has played 35 times for his country.