if you are Catholic, then you are expected to be married in the Church, not just in a civil registry office.
Please speak directly to your priest and do not get information from people who visit you. Often they are mistaken.
There is no requirement that your parents be Catholic or that your fiance’s parents be Catholic. The only persons whose religion is considered are yourself and your fiance. If you are both Catholics, then no problem; if only one of you is Catholic, then you can often still get permission to be married in the Church, if certain conditions are met. Please talk to your priest to learn more.