Watch the vid ... the man scales the 330-meter tower, making his way over the blue ring of the Olympics logo ... which is temporarily perched on the famed landmark.
The incident went down Sunday afternoon ... just 3 hours before the start of the Olympics closing ceremony, forcing French police to evacuate the area around the Tower.
It's unclear where the climber kicked off his ascent ... but he was spotted gaining some serious height around the tower's first viewing deck.
Visitors were escorted away by local police around 3 PM .