PARIS — Rachida Dati built her against-the-odds career by defying convention. So it was in character when — while serving as France’s justice minister — she had a daughter and refused to say who the father was.

Now, what was once believed to be an exercise in discretion has morphed into a messy scandal involving tales of power, sex, and ambition. Dati, now 46, says simply: ‘‘I have a complicated private life.’’