Etymology

Undoubtedly fixed as of XIIème century, when the children inherit the paternal name, the French patronyms generally claim one of the four headings:

Obviously, JACQUEMET, hypocoristic1) of JACQUES, the Christian Apostle, belongs to ultimate of the quoted categories. (in Gothic, this name écrivait:Jaqmet, the consonant < Q > being tildée).

As for can the origin of name, act of a pilgrim therefore or returned of Compostelle?

1)
hypocoristic: adjective and male noun: who is used to express an affectionate attitude.