Holders France failed to qualify for the final four of the Nations League when they slumped to a 1-0 defeat at home to Croatia as they stayed winless in the competition on Monday.
The world champions, who have now lost two and drawn two, are bottom of Group 1 on two points, five adrift of Croatia who prevailed thanks to an early Luka Modric penalty.
Denmark beat Austria 2-0 to stay top on nine points and cannot be caught by France, who are in danger of being relegated, with two games left in the group.
Austria are third on four points.
France coach Didier Deschamps reshuffled his team again as he looked to rest players at the end of the season and in all four matches this month never fielded the best possible line-up.
Les Bleus looked short of ideas in a defeat to Denmark plus draws against Croatia and Austria before Monday's loss to the team they beat in the World Cup final four years ago.
Croatia grabbed the early lead after five minutes when Modric converted a penalty after Ibrahima Konate fouled Ante Budimir. It was Modric's 22nd goal in 152 games for Croatia.
Kylian Mbappe had two opportunities but it was the visitors who threatened most in the 17th minute through Josip Brekalo.
Deschamps made two changes at half-time, bringing in Aurelien Tchouameni for Boubacar Kamara in midfield and Benjamin Pavard for Jules Kounde on the right flank of the defence.
Mbappe had another couple of chances but Ivica Ivusic saved comfortably as Croatia controlled the pace of the game.
Antoine Griezmann replaced Matteo Guendouzi with 10 minutes left in a last-ditch attempt by Deschamps to salvage a point.
But it proved in vain as France failed to score for the first time after netting in their 23 previous games.
"It was a difficult month of June in terms of results. We did not have the energy and the strength against teams who had more than us," said Deschamps.
"We lost a bit of self-confidence along the way but it's mostly freshness that we lacked. When you play so many games it is very very hard."
