The Colombians join a select club of national sides who can boast of defeating Les Bleus in front of 80,000 people at the Stade de France here on Friday, reports EFE news agency.
For France, meanwhile, their failure to protect a two-goal lead at home must be a cause for concern less than three months from the start of the World Cup in Russia.
But the opening 26 minutes belonged to the French, as N'Golo Kante smothered successive Colombia forays in midfield and Kylian Mbappe hammered again and again at the right side of the visitors' defense.
Olivier Giroud gave France the lead in the 11th minute, beating Colombia keeper David Ospina to score his 30th international goal.
Thomas Lemar made it 2-0 for Les Bleus in the 26th minute. The goal sparked protests from the Colombians, who thought the play should have been stopped earlier due to alleged foul by Antoine Griezmann.
The tide turned two minutes later.
Coach Jose Pekerman moved his lines forward and the Colombians made deeper inroads, provoking France keeper Hugo Lloris into a reckless foul against Luis Muriel.
The referee pointed to the spot and Muriel converted, cutting the French lead in half.
Colombia gained the advantage in possession, though France remained a threat on the counter thanks to the pace of Mbappe, who served up a perfect ball to Griezmann in the 39th minute only for the Atletico Madrid star to waste the chance.
The South American squad carried their new-found confidence into the second half.
Lloris was up to the task when Muriel challenged him in the 57th minute, but the equaliser came just five minutes later on a goal by Radamel Falcao, his 29th for Colombia.
The second goal for the Colombians silenced the French fans and the team likewise seemed demoralised.
With five minutes left in regulation, a foul by Umtiti against Izquierdo resulted in another penalty, converted by Quintero to complete the comeback.
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