The man, who described himself as Polish and was said by police to have mental health issues, was talked down and arrested just before 3 p.m. (1300 GMT), by which time thousands of would-be visitors had been kept waiting for more than two hours in sweltering heat.
After having reached the second floor of the monument, the man, who was around 30, attempted to climb up to the third floor from the outer part of the monument, a tower employee said.
Police sources told AFP the man, wearing John Lennon-style sunglasses, bermuda shorts and red trainers, had told them in broken English that he had wanted to be filmed by a helicopter.
Visited by seven million people every year, the Eiffel tower is the scene of regular suicide attempts, including one last year in which a British man climbed to the very top of the 324-metre tower before plunging to his death.
Tower staff refuse to divulge the exact number of such incidents every year for fear of encouraging them.