The landmark tower became the target of false bomb threats on two occasions on Saturday and was cleared of visitors each time.
Paris detectives are leading the probe into suspected “threats to lives” and “falsely claiming that a dangerous explosive incident has occurred or will occur”, the prosecutors’ office said.
The charges carry a prison sentence of up to two years for those convicted.
The threats were made via posts on gaming site jeuxvideo.com and on moncommissariat.fr, a platform for online contact between citizens and police.
The Eiffel Tower, the French capital’s main tourist magnet, attracted 5.8 million visitors last year.