I read that both of his parents were aliens, but I could be wrong. In any event, his nomination in 1856 shows that the idea that it is birth on U.S. soil, and not birth to two citizen parents, that makes a Natural Born Citizen is not a new one.
Yes, it does. Fremont was completely open about his French father. That is featured prominently in his campaign autobiography, and he habitually signed his last name with a French accent over the e.
Nobody seemed to have cared in the least.
I would be interested in where you read that, if you can easily find it again.
Wikipedia says:
Frémont’s mother, Anne Beverley Whiting, was the youngest daughter of socially prominent Virginia planter Col. Thomas Whiting. The colonel died when Anne was less than a year old.
I have assumed she was an American.