Members of the France rugby union squad are questioned by police as "potential witnesses" in a sexual assault case.
A French Rugby Federation statement said: "With their inappropriate behaviour they did not respect their status as worldwide players and the responsibilities that brings".
The official Rugby France Twitter account earlier tweeted: "The FFR confirms that some players are being heard by the Scottish authorities".
"With this inappropriate behaviour, they failed to respect their duty as global players".
Scotland lifted the Auld Alliance Trophy after beating France
A police statement said inquiries had established that no crimes had been committed and no arrests were made.
Teddy Thomas, Louis Picamoles, Arthur Iturria, Anthony Belleau, Jonathan Danty, Sekou Macalou, Remi Lamerat and Felix Lambey have all been left out.
The alleged incident occurred hours after Les Bleus had lost a pulsating encounter 32-26 against Scotland at Murrayfield - their second defeat of this campaign.
The French news site Rugbyrama said several players were seen "tipsy" in the Tiger Lily bar on George Street.
The FFR claimed that reports of the players being involved in a brawl were "false", although they did not address questions regarding reports of some players appearing to have suffered facial injuries.