Catharism (/ˈkæθərɪzəm/; from Greek: καθαρός, katharos, pure) was a name given to a Christian religious movement with dualistic and gnostic elements that first appeared in the historical record in the Languedoc region of France and other parts of Europe in the 11th century and flourished in the 12th and 13th centuries. In 1208, Pope Innocent III attempted to use diplomacy to end Catharism, but in that year, his papal legate Pierre de Castelnau was murdered while returning to Rome. This prompted the Pope into action and resulted in the Albigensian Crusade. The Albigensian Crusade sought to extinguish the movement in the early decades of the thirteenth century but was not entirely successful. When the pope realized the crusade had failed to eliminate the Catharist movement, he launched the Medieval Inquisition to finish the task.
An article arguing against Levitov's case can be found here 
There are various arguments against the case - including the VM being dated to long after the Cathars were suppressed, not appearing to have a religious aspect and there being no obvious French connection to it.