Do you have any info about the relatives of Charles or Anciet, both from St-Anicet? That would be the possible branches if there was a family connection.
My Cartier relatives were from St. Anicet. I have a Charles Cartier who actually had three wives (Adelaide Fournaise, Adelaide Saumier and Domitille Lajoie), and it's possible that the records of children are not complete. My GGGGg was a Charles Cartier living from 1793-1882 in St. Anicet. That branch is as follows:
Charles --> Olivier ("Oliver") --> Zenophile ("Sandfield", "Sanifil", "Sanfield") --> Sandfield ("Sanfield", "Sanifil") --> Harry (my Grandfather) (who was raised a Reid (mother's maiden name) not a Cartier.
Looking into some other possible links for the later generations, some of them are listed as Carty or Cartie. They moved to the Greenfield Glengarry area of Ontario (Waterloo region), then moved back to Cornwall.
Do you have any info on your Charles' wife or other children?