We present various versions of the maximum principle for optimal control of forward-backward SDEs with jumps. Our study is motivated by risk minimization via g-expectations. We first prove a general sufficient maximum principle for optimal control with partial information of a stochastic system consisting of a forward and a backward SDE driven by Lévy processes. We then present a Malliavin calculus approach which allows us to handle non-Markovian systems. Finally we give examples of applications.