Hosts the Netherlands, who beat Sweden 2-0 on Saturday, will face England who edged France 1-0 in Deventer in Sunday's last game thanks to Jodie Taylor's fifth goal at the tournament.
England's first win over France in 43 years
England scored their first victory against France since 1974 owing to Taylor's shot from the right flank which French keeper Sarah Bouhaddi deflected with her palm but could not tame.
France, who lost skipper Wendie Renard to two yellow cards, had a few good chances, but Eugenie Le Sommer headed wide and Marie-Laure Delie was denied by goalkeeper Karen Bardsley. Substitute Claire Lavogez missed from a free-kick before missing narrowly with a low left-footer, leaving France waiting for their first Euro semi-finals ever.
Proud after determined performance
"I'm incredibly proud of the players. However long that game went on we weren't going to be broken down," said England coach Mark Sampson.
"This is a French team who without a doubt are one of the best in the world, but we ground out another result."
French midfielder Amandine Henry said her team had nothing to be ashamed of.
"There were two good teams and, unfortunately, tonight we have to bow out," she said.
"It was a game decided by the tiniest margins, but that's what it's like at the top level," added French coach Olivier Echouafni.