Britain, Germany, the Netherlands and Spain have all secured their last-eight spots but, with two games remaining, GB’s aim now is to top the group.
“France fought for every inch but I’m very proud of our guys, the way we’ve fought back consistently over the last three games,” said captain David Ames.
“We have a never-say-die attitude, this team wants to fight for each other and we’re doing whatever it takes to win.
“Quarter-finals, yes, it’s a nice one – but ultimately this team wants to stand on the podium.”
Britain’s men have not won a hockey medal since their gold at Seoul in 1988.
They reached the quarter-final stage in Tokyo three years ago, losing 3-1 to India.
GB face medal contenders Germany on Friday at 19:15 BST (20:15 local time).
Britain’s women, who picked up their first win on Wednesday, face the United States at 16:00 BST on Thursday.