The Americans touched first in three minutes 30.06 seconds before the stadium announcer drew gasps from the crowd and prompted wild celebrations among the French when he announced the U.S. had been disqualified "for an early exchange".
Official results showed 19-year-old Kevin Cordes, swimming the second, breaststroke leg, had jumped early by 0.04 seconds.
"A relay disqualification is not a particular individual's fault," U.S. team member Nathan Adrian told reporters.
"It's Team USA's fault and it falls on all of our shoulders," he added.
"It will really motivate him. In the next couple of years we're going to have the fastest breaststroker in the world."
France clocked a time of 3:31.51 to take gold, with Australia winning silver in 3:31.64 and Japan bronze in 3:32.26.
The Americans were denied what would have been a 12th triumph in the event in 15 championships since the inaugural edition in Belgrade in 1973.
The drama echoed an incident at the world championships in Melbourne in 2007.
Michael Phelps' bid to win eight golds was ruined when the U.S. team was disqualified from the heats of the medley relay.
Phelps had already won a record-equalling six titles and was expected to win his final two events on the last day of competition to make it eight from eight.
He safely qualified for the 400 individual medley but lost his chance to compete in an eighth final when Ian Crocker left the starting blocks one-hundredth of a second too early.