The spectator surged from the crowd near Nadal as he was about to serve for the second set, leading 5-1. Security personnel wrestled him to the ground and quickly dragged him away. Another guard stood near Nadal, protecting him while the protester was subdued. Nadal later shook the bodyguard's hand before resuming play. The match was delayed briefly.
Moments earlier, two people interrupted play by chanting while holding a banner in the upper deck of Court Philippe Chatrier until security led them away.
Other protesters also brandishing red flares climbed to the top of the adjacent Court Suzanne Lenglen and unfurled a banner calling for the resignation of French President Francois Hollande.
Christophe Fagniez, the tournament's director of operations, later said: "The situation is under control, it's in the hands of the police."
Nadal went on to beat Ferrer 6-3, 6-2, 6-3, becoming the first man to win eight titles at the same Grand Slam event.
A male streaker wearing nothing but tennis balls and sneakers ran onto the center court and hurdled the net during the 2003 final in which Juan Carlos Ferrero beat Martin Verkerk.
In the 2009 final won by Roger Federer, a man jumped over the photographer's pit and ran on the court, went up to the Swiss player and tried to put a red hat on him. Federer brushed the man aside before security guards got close enough to intervene. After hopping the net, the man was tackled and jailed for questioning.