An investigation was opened without any public announcement on 22 June, Le Parisien newspaper revealed on Wednesday.
Some 20 "very threatening" messages, including death threats, were posted on the paper's Facebook page over three or four days in mid-June, Le Parisien reported.
They indicated that several of the paper's journalists would be murdered, the daily said.
A further threat was received by post.
Legal sources confirmed the reports to Reuters news agency.
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