The unnamed woman "spoke of a rape and named the aggressor" during the filming, the judicial source said, adding that the claims were being treated with caution at this stage.
The actual death, which took place at a station in Egly to the south of Paris, was removed by Periscope but some of the video leading up to the suicide was still available on YouTube.
At one point the victim is seen on a couch, saying the video is "not designed to create a buzz... But to make people react, to open their minds, and nothing else".
Periscope is a smartphone application that allows users to stream live video via their Twitter account. The video remains accessible for 24 hours.
An investigation has been opened into the circumstances of the suicide.
"Analysis of the telephone and recovery of the video are ongoing," said the source.
Police said they were informed by someone watching the Periscope stream.
"We were alerted around 4:30 pm by a Periscope user who was connected with the victim and told us that she was not well," a police source said.
Twitter, which bought Periscope in 2015, said it did not comment on individual accounts.
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