The teenager from the department of Haute-Savoie in southeastern France was arrested on Tuesday, said the anti-terrorist prosecutor's office, adding a probe had been launched on Wednesday.
The teenager was arrested "following his statements on social media announcing his intention to make an explosive belt with a view to dying a martyr," the anti-terrorist prosecutor's office said.
During a search of his parents' home, handwritten papers were discovered in which the teen had pledged allegiance to the Islamic State group, a police source said.
According to the same source, the teenager admitted to having planned to commit a "terrorist act" using a gun or explosive belt at La Défense, the business district west of the capital that is also home to an arena hosting swimming and water polo competitions during the Games.
The anti-terrorist prosecutor's office said work was under way to determine the teen's exact intentions.
The DGSI, France's domestic intelligence agency, is conducting an investigation.
France is hosting the Olympic Games in Paris from July 26th to August 11th, with security during the event a major concern.
In March the government raised its terror alert to the highest level.
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