2 more elements :
1 ) iata captation :
2 ) Captation from italy montreal consulate : ( see the pdf here , page 16 :
https://consmontreal.esteri.it/Consolato_montreal/resource/doc/2018/06/sito_fr.pdf ) , this document sugess that travel document holder should ask for a visa .
in conclusion, we note that this story is not clear ... the consulate can say that there is no need for a visa ...
but in the end, the flight attendant will refuse your boarding when you go chekin.
as long as the story is not clear:
do not take the risk of direct flight to rome ... frankfort is better ... (and all European capitals are easily connectable in tgv ... the rail network is very devellope in europe, and has nothing to do with canada ).