Draped in flags, the victorious team members hugged one another, posed for photos and shared emotional moments with wives and girlfriends.
Among them was Spaniard Sergio Garcia, who embraced his wife Angela in the middle of the green after beating Ricky Fowler to become the most successful player in Ryder Cup history.
He then sobbed as he was called a “legend” by team-mate Justin Rose.
“I don’t usually cry, but I couldn’t help it, what a week,” he said Francesco Molinari was also surrounded by adoring fans after securing the winning putt against Phil Mickelson at Le Golf National, outside Paris.
He also became the first European to win five points in one tournament.
The Italian, alongside Englishman Tommy Fleetwood, had spearheaded Europe’s charge against what many believed to be the strongest ever American team.
Molinari said after the victory: “It means so much more than majors, more than anything. It’s hard not to get emotional.
“They had probably the strongest team ever and we were just so good. It is unreal.”
Elated Fleetwood, 27, was carried on the back of fellow Englishman Ian Poulter, who later delighted crowds by wearing a pillar-box fancy dress outfit.
His nickname is “The Postman” as he always delivers points for the team, including beating world number one Dustin Johnson. Englishman Paul Casey, who made one of the best shots of the day, celebrated with his wife Pollyanna.
Northern Irish legend Rory McIlroy, who was with his US wife Erica Stoll, led the cheers with the 70,000-strong crowd, before Danish captain Thomas Bjorn embraced each of his players.
As he collected the trophy, he said: “They have been amazing, the 12 of them, unbelievable. “They were determined to set out and do the job themselves.
“For me it was an easy job to guide them in that direction.”
The Europeans started the day needing just four and a half points to seal victory.
The American team briefly threatened a fightback after starting strongly, but were unable to sustain a serious challenge.
Spaniard John Rahm beat Tiger Woods in a crucial match.
He said: “To beat Tiger, one of the all-time greats, if not the greatest, at a pivotal point, it is the best feeling of my life.”