The Arsenal player admits defeat could have severe consequences for Les Bleus, in a group which also contains Sweden and co-hosts Ukraine.
"Our first match is like a final for us," the 26-year-old said in the Daily Mirror. "To play against England is the worst possible draw but it will be a enormous chance for us to progress if we win.
"We can't afford to lose. Normally you might expect France and England to qualify for the second phase but football never works like that.
"We know this is like a final because defeat would be a disaster."
Koscielny could find himself up against two of his Arsenal team-mates in the England squad.
One player he will not be facing though is Manchester United striker Wayne Rooney, who is suspended for the first two games.
"The absence of Rooney is a joy to us," Koscielny said. "He is a brilliant player, such a talent.
"But England have quality.
"It will be strange to play against Theo Walcott and Alex Oxlade-Chamberlain. But Arsenal is one thing, France another.
"We've had a lot of jokes about playing against each other from being on the pitch together and in training at Arsenal.
"But while we laughed and joked, when the game comes it will be very serious and we must win the game. We all know that."