The man, who has not been identified, had been climbing up the statue which represents liberty in the middle of the vast square in north-east Paris, but "slipped", a police source told AFP.
It marked the first serious accident during the Techno Parade music festival, now in its 17th year.
"The incident occurred after the conclusion of the Techno Parade," said a visibly shocked Mr Tommy Vaudecranne, president of Technopol, which organised the event.
"All of the floats had already left the Place de la Republique."
He continued: "Our hearts go out to the family and relatives of the deceased."
A video of the man falling off the statue was circulated on social media, sparking controversy among Twitter users.
Though dangerous, the sight of young people in Paris climbing up onto statues, roofs and the tops of bus shelters during music festivals and parades is not uncommon.
The Techno Parade music festival is an annual celebration of a form of music that is still frowned upon in French officialdom. This year's edition drew thousands of revellers and featured 60 DJs and more than a dozen floats.