The incident at the world-famous tourist site was initially treated as a criminal matter, but was later designated a counter-terrorism case because of the suspect's statements to police and his apparent radicalization, the source said.
It reopened to tourists as usual on Sunday morning.
An anonymous French security source told the agency that the assailant claimed he was encouraged to try and attack a soldier by an Isis member he had recently been in contact with.
The man was arrested and is being held for questioning, and an investigation was opened by prosecutors.
Grand Canyon Rangers Find Body Believed to be Missing Woman
Her backpack was found near the South Kaibab Trail, which the park official says has no water accessibility and nearly no shade. PHOTO: Sarah Beadle, 38, of Fort Worth, Texas, disappeared while hiking in the Grand Canyon National Park, Arizona.
The man wanted to attack a soldier after encouragement from Islamic State, according to a source close to the investigation.
The man, a Frenchman born in 1998 in Mauritania living in the Val-d'Oise (northern suburbs of Paris), was "very quickly mastered and arrested" without causing any injuries, the report said.
The incident happened about half an hour before the Tower normally stops admitting visitors.
Monuments in the French capital have occasionally been evacuated for security reasons, as the country remains on alert after deadly attacks since 2015. The Eiffel Tower was lit up with team colors in celebration of the record-breaking $520 million acquisition of Brazilian star Neymar.
The man kept was wearing a Paris Saint-Germain football shirt.