In Saturday's incident, the suspect tried to force his way into the secure zone beneath the tower, held out a knife and said "Allahu akbar", the Arabic phrase for "God is great", an official close to the investigation said.
The suspect's statements to investigators and his radical views led the anti-terrorist section of the prosecution to take over the investigation, a judicial source in Paris said on Sunday (Monday NZ Time).
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.
He said he wanted to attack a soldier.
City authorities plan to replace the makeshift barriers now surrounding the Eiffel Tower with bulletproof glass walls on two sides, and metal fences on the other two.
The legal source said the man with the knife, a Frenchman born in the West African state of Mauritania, had been discharged from a psychiatric hospital in July.
No one was injured and the tower was evacuated at 11:30 p.m., about half an hour before the tower stops admitting visitors.
France has been in a state of emergency since November 2015 and has seen a string of attacks on security forces who have been regularly targeted, particularly those guarding key tourist sites.
A screen near the bottom of the tower displayed a message welcoming Brazilian star Neymar to the club.
When arrested on Saturday night, the man was reportedly wearing the colors of the Paris Saint-Germain soccer team.