I'm not quite sure where the g came from (it might be from a dialect loanword). The term in Italian for an inhabitant of Parma is parmense which looks like a learned borrowing from Latin (usually -ensis > -ese in Italian, cf. Verona ~ veronese, Genova ~ genovese). Remember the English did all kinds of things to placenames. My favorite is Leghorn from Livorno. My grandmother always refered to parmesan cheese with the Ligurian dialect word piaxentin /pijaʒentiŋ/ not because we used cheese from Piacenza on our pasta, but because her mother no doubt did back in Genova, although for pasta al pesto pecorino romano or sardo is used. Hmmm, pesto.