The office of the National Finance Prosecutor has confirmed to Press Association Sport it is looking into last week's 6-1 victory by the French champions, in the same group as Liverpool and Napoli.
However, a spokesperson for the PNF declined to comment further.
French newspaper L'Equipe claimed UEFA alerted the French authorities to a possible manipulation of the scoreline in the game days before the fixture took place.
L'Equipe allege a credible source reported an unnamed Red Star official bet around £4.3million (5 million euros) on the Serbian club losing by five goals at the Parc de Princes.
Red Star have reacted angrily to the allegations.
"FC Red Star with the highest anger and abomination rejects the story L'Equipe published today about (the) suspicious result of the PSG vs Red Star match and involvement of anyone from our club in possible wrongdoings," said a club statement.
"The article can harm and bring big damage to our club's reputation and that is why we insist that UEFA and investigators in Serbia and in France investigate the whole story and get the truth.
"Today's technologies and other mechanisms are so improved that it is basically impossible to leave this case unsolved.
"Red Star expects to get the truth at short notice and remove any doubt about our involvement in possible wrongdoing."
PSG have also responded to the allegations.
"It is with utmost amazement and indignation that we have learned of the information that you have shared," the club said in a statement to L'Equipe.
"At no time has a member of the club been asked to discuss any matters other than those strictly related to the organisation of the match, namely meetings, visits and other standard lunchtime protocol in the build-up to Champions League matches."
