The incident happened late in the first half at the Stade Marcel Michelin.
The offence was ruled to be at the low end of World Rugby's sanctions and 12 weeks was selected as the entry point.
But the 23-year-old's good disciplinary record, remorse and relative youth led to the penalty being reduced.
The French prop's ban means he will miss seven Top 14 matches and the European Champions Cup games against Bordeaux-Begles and Exeter before he is eligible to play again on 20 February.
The incident was spotted by Welsh citing commissioner Jeff Mark while the independent disciplinary committee was made up of  Jeremy Summers (England), Jean-Philippe Lachaume (France) and John Carroll (Ireland).
Clermont won the game 38-19 to remain in control of Pool Five and damage Ulster's prospects of making the knockout stage.
Clermont Auvergne's Etienne Falgoux has been banned for seven weeks for making contact with the eye area of Luke Marshall in Ulster's Champions Cup loss on Sunday.