Serbia last won this tournament two years ago in Madrid, Spain and head coach Vladimir Jovanovic was elated - although at the same time at a loss for words - afterwards.
"This is fantastic, a great win for us, a great performance," he said with a broad smile on his face.
"We are the best in Europe, it's a great feeling," enthused Nemanja Jamaraz, who made a key steal and free-throw to stop France's comeback late in the game.
France head coach Philippe Ory was graceful in defeat.
"Serbia played better than us, no doubt about it. We played well in stretches but missed too many shots close to the basket and you can't expect to win when that happens," he said.
"But this was a great tournament for us. To play in front of our fans and get to the final, it's extraordinary. A memorable experience."
Serbia led by as many as 12, 63-51, when Danilo Andjusic hit consecutive three-pointer early in the final quarter, but France rallied back to get within one, 69-68 on Evan Fournier's lay-up with 2:12 left to play.
Serbia replied with Andjusic hitting a free-throw and Lazar Radosavljevic burying a vital three-pointer from the corner for a 73-68 advantage.
Fournier made a tough lay-up to cut the deficit to three, 73-70. Jaramaz then missed a jumper and Henri Kahudi found Mael Lebrun on the fastbreak but he lost control of the ball and Jaramaz got the steal. He was fouled and made one of two free-throws with 33 seconds left.
France got within two, 74-72, on Fournier's pair of foul shots with 25.8 seconds to go, but that would be the closest they would get.
Andjusic was fouled and made good on his two attempts from the charity stripe. Nikola Stojiljkovic launched - and missed - a questionable three-pointer with about 17 seconds to go and Branislav Djekic sealed the result from the free-throw line.
Andjusic finished with a game-high 22 points - including five three-pointers - and Djekic added 16. Dejan Musli had 14 points, 14 rebounds and three assists.
Lebrun had 17 points for France and Fournier added 16.
Serbia score eight of the first 10 points in third quarter to extend their lead to 48-37, but France used a 7-0 run, started by Mael Lebrun's three-point play and capped off by Frederic Mondesir's consecutive lay-ups, to get within four, 48-44.
Musli then made a pair of free-throws and Lebrun threw down a savage dunk on the Serbian big men - much to the crowd's delight - to make it a four-point game once again, 50-46.
Danilo Andjusic hit a three-pointer at the other end and, when Nikola Stojiljkovic made a free-throw to once again cut the deficit to four, 53-49, Serbia replied from long range courtesy of Djekic.
Geoffrey Renon got a friendly role on his top of the key jumper and Jaramaz hit a free-throw for a 57-51 score to end the third quarter.
Serbia used an 8-0 run to jump in front 10-6 in a low-scoring first quarter. France were within one, 12-11, courtesy of Fabien Paschal's tip-in off Frederic Bourdillon's missed lay-up with 1:35 left in the period.
But the hosts had two costly turnovers and trailed by five, 17-12, after Andjusic scored four quick points in the last minute, including a three-point play at the death.
Serbia extended that advantage to seven, 19-12, on Musli's dunk early in the second quarter. And they were soon up by as many as 11, 26-15, when Musli beat Vincent Pourchot down the court in transition for a dunk with just over eight minutes remaining in the half.
Spurred on by their fans, Les Bleus fight back and seven unanswered points see them close within four, 26-22, on Geoffrey Renon's basket.
And they would get within three on Renon's free-throws but Branislav Djekic then scored seven quick points for a 38-30 advantage.
Nicolas Stojiljkovic buried a wing three-pointer buried a three-pointer from the wing to cut it to five, 38-33, and Nemanja Jamaraz and Fournier traded free-throws to end the half.