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The prosecutors' office said on Tuesday the investigation into "fraud in an organised group" and "active and passive corruption", was related to a doubles match between Romanian pair Andreea Mitu and Patricia Mari and Russian Yana Sizikova and American Madison Brengle.
The Romanians won the match before being knocked out in the third round.
When asked about the case, the French Open organisers referred Reuters to the Tennis Integrity Unit (TIU), which said it was aware of the investigation but declined to comment.
The investigation, which was opened on October 1, is being handled by the French police's Central Service of Races and Games (SSCJ).
Alexei Selivanenko, vice president of the Russian tennis federation, had told the Championat.com news website on Sunday: "As long as there are no official documents, it is too early to comment on anything. Tennis has a zero-tolerance policy for cases of this kind."
The Russian tennis federation had no additional comment on Tuesday. Brengle and the Romanian pair, and their respective tennis federations, could not immediately be reached for comment.
The long shutdown in global sport due to the novel coronavirus meant players were unable to earn money, potentially heightening the risk of corruption.
The TIU was set up in 2008 to tackle the threat of corruption in the game and has the power to issue life bans for serious offences.
Alerts flagged up to the TIU increased in the first quarter of 2020, but these cases rarely involve the ATP or WTA Tour events or Grand Slams. Most TIU convictions concern players plying their trade in the lowest rungs of professional tennis.
The TIU said it had received 38 match alerts between January and March this year, compared with 21 in the same period in 2019.
In its most high-profile case, the TIU in 2018 suspended Argentine tennis player Nicolas Kicker for six years - three years of it suspended - and fined him $US25,000 ($NZ37,900) for match-fixing and other offences.
The player had been ranked 78th in the world less than a year before his suspension.