The offences occurred in an 18-13 French quarter-final win over Ireland in Exeter on Sunday.
Lock Feleu was given a yellow card for a high tackle and faces a three-match ban. Flanker Berthoumieu could be out for 12 matches after being found guilty of sinking her teeth into Irish star Aoife Wafer.
If the bans are confirmed, the World Cup will be over for both women, as France have a maximum of two matches left, starting against England on Saturday in Bristol.
Irish captain Sam Monaghan had complained to the referee early in the second half that Berthoumieu had bitten Wafer.
The replay official could not confirm the offence, but videos on social media caught the deed.
Both offences were reported by an independent World Cup commissioner, Jeff Mark from Wales.
Both players had acknowledged their offences. Both appealed the bans.
Those appeals will be heard on Tuesday by a disciplinary committee, World Rugby said in a statement.