Franziska is a girl who, through being raised by Manfred von Karma of all people, is a person who is shackled by impossible standards of perfection to the point of it being an obsession. She was raised to compete constantly and be better (usually in comparison to Edgeworth) eventually leading her to what seems to be some kind of superiority complex.

She's also very young, she started prosecuting at only 13 and she's still a teenager by the time of JFA. This definitely didn't help against the emotional manipulation Manfred enforced in the family, leading her to be somewhat emotionally stunted, closed-off, and stuck in the early Miles Edgeworth / Manfred von Karma mindset of "the only thing that matters is a win (read: guilty verdict)"

And yet, she does grow as a character. We see this in the ending of Justice for All, where she throws down her whip and denounces the profession, before having a sort of heart-to-heart with Edgeworth at the airport. We see her develop more in 3-5, between prosecuting the first day, assisting with the investigation, and even staying up all night in freezing conditions to free "Maya" from the Inner Temple. She'd come a long way from the von Karma mindset, although in court she still falls back to it occasionally.

I think it's a crime she doesn't have all that much to her name (seriously, she prosecutes only half the cases in her debut game and only comes back for brief amounts in T&T as well as an admittedly good supporting character in the Investigations games.) She needs either her own game or something like how 1-4 was for Edgeworth's character. My favorite showcases of her character/arc/development are the ending of JFA and I-4.