The French Rugby Federation is to begin an official inquiry into the Mathieu Basteraud affair after the team arrived in France on Tuesday.
The 20-year-old player initially claimed he had been assaulted outside his Wellington hotel during the French tour of New Zealand in June.
Investigations by Wellington police then forced team management to say Basteraud hit his head on a bedside table.
Team manager Jo Maso then suggested Basteraud's injuries came about after a fight among players.
Major French newspapers are questioning the veracity of the accounts given so far and believe sackings could result, given Maso's suggestion.
It appears Maso, delegation chief Jean Dunyach and the team's doctor could face the sack over the matter, which the French Rugby Federation says has cast a shadow over it and the game.
Basteraud is under observation at a psychiatric hospital.