Three wins and two losses for Sweden meant they finished behind Italy and France in the group and will now travel to face another of the co-hosts in the Round of 16, as they meet Czech Republic in Brno on either 30th or 31st August.
Coming from two sets down to beat Croatia last time out had assured the Swedes of a place in the knockout stage, while France came into this having lost their unbeaten run to Italy.
Sweden's chance of causing an upset seemed to have come and gone when they levelled the first set at 24-24, only for France to get over the line and win 28-26. However, the home side dominated the second set, building a healthy lead before finishing with a 7-1 run to win 25-13.
But France, whose best finish at the European championship was sixth in 2023, responded well and took a six-point lead in the third set before maintaining a healthy advantage and going ahead again in the match with a 25-20 success.
Roared on by the home crowd for the final time, Sweden came from behind in the fourth set as they looked to secure a third five-set win of the tournament. The lead changed hands several times, but it was Sweden who missed the chance when 24-23 up, and France got themselves in front again and secured another 28-26 set win to take the match, 3-1.
France will also head to Brno for their first knockout match, as they take on Greece. All four host nations - Sweden, Czech Republic, Azerbaijan and Turkey - have made it through the Group Stage.