"There is a strong likelihood that the suspects fled by parachute, in the morning, before the arrival of security teams," a police source told the French newspaper Le Figaro.
The alarm was raised after guards at the tower spotted the three men climbing the structure via video surveillance. The police and the tower security service undertook a systematic search of the tower, using a team of police dogs trained in detecting explosives, which found no sign of the intruders.
The Tower eventually reopened at 1:30 p.m; police theories as to the group's motive include the possibility of an attempted terrorist attack, or that the intruders were extreme sports enthusiasts who wanted to jump from the structure.
The landmark has in the past been targeted by terror plots, including an al-Qaeda plot uncovered in July 2014 to target a string of landmarks, including the Louvre, the Eiffel Tower, and a nuclear power plant.
The 324 meter tall Eiffel Tower was one of the sites assigned special protection from the French armed forces as part of the Vigipirate security put in place after the Charlie Hebdo terror attacks in January 2015.
The Tower attracts almost seven million tourists each year, and is France's second most visited monument, after the Notre Dame Cathedral in Paris.