Sometimes when I pray behind the Imam, the
Imam will start reading the fatihah almost immediately. Should I finish the opening du’a,
or stop and listen to the Imam’s recitation?

What you should do is listen to the imaam’s
recitation, because Allaah says (interpretation of the meaning): “So, when the
Qur’aan is recited, listen to it, and be silent that you may receive mercy.”
[al-A’raaf
7:204].

And Allaah knows best.