Since her mother was a human and her dad was a frog, it makes sense that Fiona was born a half-human, half-frog hybrid, which is what an ogre is. So was she cursed to be human?
There is no evidence in the films to support this.
- The storybooks at the beginning of Shrek 1 and Shrek 2 clearly show both Fiona and King Harold to have been perfectly human at the time of Fiona's birth.
Fiona's discussion with Donkey in Shrek 1 strongly indicates that her ogre form was the result of the curse, rather than her natural state:
FIONA: When I was a girl, a witch cast a spell on me. Every night, I become this... this horrible, ugly beast.
Fiona's entire motivation for marrying Lord Farquaad in Shrek 1 was to obtain a true love's kiss from him and break the curse. If the human side was the curse, she would not - at that point - have wanted to assume that form permanently. She doesn't become comfortable with her ogre form until she realises that Shrek loves her even in that form, whereas Farquaad doesn't love her at all.
- When Prince Charming arrives at Fiona's tower at the start of Shrek 2, and encounters the wolf sleeping in Fiona's bed, he seems to seriously believe for a moment that he might be Princess Fiona in her cursed form (and expresses relief that he isn't). This strongly suggests that he doesn't know what Fiona's cursed form actually looks like, which wouldn't make sense if she was cursed to be human.
- King Harold's racism towards Shrek throughout most of Shrek 2 would make even less sense if Fiona had been born an ogre. Why would you father an ogre if you hated them (or alternately, why would you hate ogres if you had fathered one)?
In addition to what F1 noted, it's worth noting that in Shrek 2 we see that Fiona's diary has her pining to be "normal" again so she can be like the other princesses (she's disappointed she can't attend Sleeping Beauty's slumber party). She then practices writing "Mrs. Fiona Charming", for comedic effect
Given Charming was expecting beautiful woman to kiss, this also doesn't fit. Clearly Charming wasn't expecting to marry an ogre.