The 29-year-old hurt his tibia in Friday night's 64-0 thrashing of Calvisano in the European Challenge Cup.
Club coach Jake White said Trinh-Duc had undergone a scan on Monday afternoon, which revealed a fracture of the tibia, the source said.
Trinh-Duc suffered that same injury just over a year ago against Oyonnax, which cost him five months of the season.
He may not play again before the start of the Six Nations, which would impinge on his ability to add to his 50 France caps.
Although rarely picked by Philippe Saint-Andre, Trinh-Duc was hoping to force his way back into the France fold now that Guy Noves has taken over following France's disappointing World Cup.