Police Scotland says French rugby players were interviewed as "potential witnesses" after reports in Scotland's Herald newspaper of an incident at a bar following the French defeat to Scotland in the Six Nations on Sunday.
Scotland beat France 32-26 in a thrilling Six Nations encounter at Murrayfield to move fourth in the table behind Ireland, England and Wales.
France's plane was stopped before take-off and and was grounded on the tarmac at Edinburgh Airport.
France's flight back to Paris from Edinburgh has been delayed on Monday as Scottish police are understood to have removed several players from the plane for questioning over an alleged brawl in Edinburgh on Sunday night.
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Police Scotland said inquiries had established no crime had been committed and no arrests were made.
According to the French rugby website Rugbyrama, the incident took place as a group of players were leaving Edinburgh's Tiger Lily bar.
Police halted their flight from Edinburgh Airport at 11am in order to pursue their enquiries but later confirmed that no crime had been committed.
The official Rugby France Twitter account earlier tweeted: "The FFR confirms that some players are being heard by the Scottish authorities".
Initial allegations of a bar fight were dismissed by police, who said they have not received reports of such an incident.