|Evanthia Maltsi guarded by Sandra Le Drean|
The tournament hosts battled bravely but a late fightback came up just short in the final minute.
After cutting France's lead to 73-70 with 47 seconds remaining, a timeout was called and Greece coach Giorgos Tsitskaris instructed his players to go into a fullcourt press.
France inbounded the ball to Cathy Melain and while Greece tried to force a steal, a player bumped the veteran co-captain.
Melain went to the free throw line and made both shots for a five-point lead, accounting for the final score.
A disappionted Tsitskaris, whose team would have advanced to the last eight had they pulled off the upset, suffered their second close defeat in two nights. Greece were beaten 72-67 by Serbia & Montenegro on Tuesday.
"We lost again by five points and we are out," Tsitskaris said.
"My players tried their best against the European Champions. We made one crucial foul with 47 seconds on the clock and that is why we lost."
Audrey Sauret and Sandra Le Dréan paced Les Bleues with 20 points each while Evanthia Maltsi had 16 for Greece.
"We're out but we played well in the last two games," Maltsi said.
"Other teams had more experience and we paid for that. We tried and we wanted to win very much. We have to take the experience and use it for 2004 in Athens."
Greece will be in next summer's Olympics since they are hosting the event.
France coach Alain Jardel, despite having a team in the quarter-finals, seemed to envy the Greeks in his post-match press conference.
"Greece have already qualified for the Olympics but we do not know if we will be there," he said.
Sauret had kind words for the opponents.
"I want to congratulate Greece, because I love teams that play with heart like they do," she said.