A spokesman for Houston police said two tablets found on Robert were believed to be the sedative Xanax, but the climber denies this.
"I was only using prescription medication called Urbanyl, which is an anti-epileptic," Alain Robert, 43, said after climbing the 308-foot Paris tower in approximately 20 minutes. "This is my way of issuing a denial."
Alain Robert's next court appearance is scheduled for Jan. 4 in Houston but he says he will be in Mexico at the time, doing what he is famous for - climbing.
Alain Robert is known for climbing some of the world's tallest buildings, including the Eiffel Tower, the Empire State Building and Kuala Lumpur's Petronas Towers. Alain Robert climbs using only his bare hands and with no safety net.