4 PLAUSIBLES THEORIES :
We can read in the baptism of Charles Savoie in 1703, than his father and mother were alived in the event and they were there. No body knows how to sign at the time. Germain being the son of Francois Savoie would have learned to sign if his father had a noble education.
This is almost completely factual.
So it is almost certain that François Savoie himself may not have known how to write. So if we keep the theory that Thomas was his father, in my opinion and with the deduction of all these documents, he must indeed have been a child declared illegitimate of Thomas by a middle-class mother of lower rank or even a roaster. We can really put aside any theory about François' mother and even more that it was a Bourbon.
So 4 logicals theory cases arise:
1. François Savoie was the illegitimate son of Thomas Savoie of Carignan and a peasant mother. He was certainly not recognized by the father, certainly did not enter into any connection with him either during his childhood. And question of hushing up the affair, he was sent to Acadia to dispel court gossip about his father's low morals, who were more targeted during this period.
2. François was the son of peasants who bore another name and the name Savoy was given to him to designate his origin like many Canadian settlers. In this case, he was simply from Savoy and it was a nickname for his native land.
3. A false claim of paternity from the mother of François in France for gain some money or some notoriety. It could has been a bad affair to lie like this about a high ranking noble but this theory is a plausible one too.
4. He was from an other house of Savoy and illegitimate son too (This theory is in last position cause if the dead bed confession really existed, this theory sink).
We cannot rule out either of these 4 theories at this time.