Jacques Brunel's side were leading the hosts for much of Sunday's game, only to surrender their advantage in the closing stages and slip to a second successive defeat in this NatWest Six Nations.
According to Le Parisien newspaper Louis Picamoles was one of the players hauled off the plane.
A police spokesman told the Press Association news agency that the French players were questioned in connection with a report of a sexual assault in downtown Edinburgh early Monday following Scotland's 32-26 win over France in the Six Nations.More news: MI officer shot during barricaded gunman incident
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Police said their inquiries had established that no crimes had been committed.
Members of the squad are said to have been escorted off a plane departing Edinburgh Airport on Monday morning.More news: Boston Celtics: Concern sets in following blowout loss to Cavs
However, the players were actually questioned as "potential witnesses" after the police received a report about a possible sexual assault in Edinburgh city centre in the early hours of this morning.
Cops launched a probe and spoke to a number of the France stars before establishing no crime took place. "We are waiting for more information", the FFR said on Twitter.
Events Manager Jo McKinnell confirmed that the French players were in the bar that night but said there were no incidents.More news: Pakistani Taliban senior commander confirmed killed by United States drone
Reports in France had suggested police became involved following an incident in the Tigerlily bar on Edinburgh's George Street on Sunday evening.
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