France's flight back to Paris on Monday was delayed after police removed several players from the plane for questioning over an incident in Edinburgh on Sunday night.
Initial reports in the French and Scottish media suggested the players were questioned over an alleged brawl, reportedly with Scottish supporters, at the end of a night out in the Scottish capital following their team's 32- 26 defeat at the hands of Scotland in the Six Nations tournament.
But a statement from police later on Monday said the players were questioned as "potential witnesses" to an alleged sexual assault.
"Following an initial report of sexual assault in Edinburgh city centre during the early hours of Monday 12th February police conducted various lines of inquiry, including speaking to a number of potential witnesses," a statement from Police Scotland said.
"These inquiries have established that no crime has been committed."
France's Rugby Federation earlier confirmed that several players were being questioned by police and that they were waiting for more information.
La FFR confirme que certains joueurs sont entendus par les autorités Écossaises. Nous sommes en attente de plus d'informations.— FF Rugby (@FFRugby) February 12, 2018
Reports suggest the French rugby team's coach Jacques Brunel had given his team the green light to go for a drink in the centre of Edinburgh on Sunday night.
The French news site Rugbyrama said several players were seen "tipsy" in the Tiger Lily bar on George Street.
The site claimed that on returning to the hotel that members of the team were involved in a fight with Scottish supporters, but this was not confirmed by police.