Charles Henderson on his marriage with Marie Théotiste Thérien did not have his parents named on the record. All that is said of him is that he was a bachelor, of age, resident of that parish (Château-Richer). His wife and another woman sign the record, he does not.
As far as the Anderson bit, it's a frequent similar name, and the records for the children show it sometimes, variations that appear are Enderson, Anderson and of course Henderson. Those are pretty much all in the St-Roch parish of Québec city.
Marie Théotiste remarried on 28 Apr 1869 to widower Charles-François Beaupré in St-Sauveur parish church of Québec city. Her deceased spouse is listed as Charles Anderson there.
Casting about for a possible birth for him, I find only one Charles Anderson born 25 June 1810, baptized 7 Aug in Châteauguay, to Charles Anderson and Marie Abel. No other baptism shows up in Catholic records. If he was another denomination, that could get complicated finding a record. My search included Henderson variation.
As a note, the Charles Anderson I found was a twin. Don't twins run in families a lot? Your man's son François-Xavier-Gaudiose was a twin.