Olivier Christen said the plots included plans to attack "Israeli institutions or representatives of Israel in Paris" during the Games, which ran from July 26 to August 11.
The prosecutor told broadcaster France Info that "the Israeli team itself was not specifically targeted".
In all, five people, including a minor, were arrested on suspicion of involvement in the three foiled plots against the Summer Games, which were held against the backdrop of the Israel-Hamas war and Russia's war in Ukraine.
The suspects faced various terrorism-related charges while they remained in pre-trial detention, the prosecutor said.
France was on its highest security alert in the months before the Olympics and Paralympics, which wrapped up last week.
During preparations, Interior Minister Gerald Darmanin repeatedly warned that security threats included those from Islamic extremist groups, violent environmental activists, far-right groups and cyberattacks from Russia or other adversaries.
In May, members of the General Directorate of Internal Security arrested an 18-year-old man from Chechnya on suspicion of being behind a plan to attack Olympic football events that were held in the southern city of Saint-Etienne.
The planned attack was to target "bar-type establishments around the Geoffroy stadium", the prosecutor said.
The suspect is accused of planning "a violent action" on behalf of the so-called Islamic State group's jihadist ideology.
Jihadists threats dominated the foiled plots and 80% of legal proceedings against suspects include the extremist ideology that still influences France's youth, the prosecutor said. IS continues to "spread propaganda," he said.
Preventative measures included increased house searches and house arrests before the start of the Olympics, the prosecutor said, adding that police and other security personnel conducted 936 house searches so far in 2024, compared with 153 in 2023.
