Ireland captain Sam Monaghan raised the issue with the referee in the second half of the match, which France won 18-13 to reach a ninth World Cup semi-final.
"Aoife told me, I didn't see it myself, but I spoke to the referee and asked them," Monaghan told reporters.
Berthoumieu's teammate, Manae Felu, has also been cited for a separate incident.
"France's Axelle Berthoumieu and Manae Feleu will have cases reviewed by an independent Foul Play Review Committee on Monday ... following two separate citings arising from the France v Ireland at Women's Rugby World Cup," World Rugby said in a statement.
"Back row Axelle Berthoumieu has been cited for an action contrary to Law 9.12 (biting), while second row Manae Felu has been cited for an action contrary to Law 9.13 (dangerous tackling)."
According to World Rugby's disciplinary code, if a player is found guilty of biting the starting point for a suspension is 12 weeks for a low-end offence.
France face England in the semis in Bristol on Saturday.