Police Scotland spoke to a number of potential witnesses at Edinburgh Airport on Monday morning, grounding the plane carrying the French squad while police inquiries were carried out.
"With their inappropriate behaviour they did not respect their status as global players and the responsibilities that brings", the French rugby federation said in a statement.
Members of the French rugby union squad which lost to Scotland on Sunday are being "interviewed by Scottish authorities" after reports they had been involved in a brawl, the French federation (FFR) said on Monday.
"They did not respect their status as worldwide players", the governing body added in a statement.
Anthony Belleau, Jonathan Danty, Arthur Iturria, Remi Lamerat, Felix Lambey, Alexandre Lapandry, Sekou Macalou, Louis Picamoles and Teddy Thomas have all been dropped from the squad, with eight new faces called up to a 32-man squad.
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Executive chairman of Remington Jim Geisler, commented, "Difficult industry conditions make today's agreement prudent". Private equity giant Cerberus Capital Management acquired Remington in April 2007 for $370 million.
However, the FFR did not name the players sanctioned.
The flight was said to have departed after a two-hour delay.
Police Scotland later issued a statement confirming that their enquiries established that no crime had been committed.
Reports on Monday suggested that the incident had taken place at the Tigerlily on George Street, as the French team mingled with supporters on a night out.
Les Bleus' Scotland defeat followed a dramatic 15-13 loss to Ireland in Paris, to where they return a week on Friday as they attempt to get off the mark against the Azzurri.