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.
Police Scotland have since stated that their investigation concluded that no crime was, in fact, committed.
The French rugby federation confirmed in a brief statement that some players were questioned, but did not elaborate.
The flight, which was due to leave at 11am, eventually took off from Edinburgh Airport at 1pm with all the players believed to be on board. "We are waiting for more information", the FFR said on Twitter.
La FFR confirme que certains joueurs sont entendus par les autorités Écossaises.
The French squad had been due to leave Edinburgh Airport on Monday morning..
The police report was made following the French team's defeat by Scotland in the Six Nations on Sunday. Nous sommes en attente de plus d'informations.
"These inquiries have established that no crime has been committed".
L'Equipe are reporting that the squad's specially chartered plane home is now stuck on the tarmac at Edinburgh Airport.
Reports suggest the "France 7" may have to remain in Edinburgh with an FFR official, with remainder of squad allowed to fly home.
According to the French rugby website Rugbyrama, the incident took place as a group of players were leaving Edinburgh's Tiger Lily bar.