Recently Buckdahn et al. (Mean-field stochastic differential equations and associated PDEs, arXiv:1407.1215, 2014) studied a mean-field stochastic differential equation (SDE), whose coefficients depend on both the solution process and also its law, and whose solution process (Xt,x,Pξs,Xt,ξs=Xt,x,Pξs|x=ξ), s∈[t,T],(t,x)∈[0,T]×Rd,ξ∈L2(Ft,Rd), admits the flow property. This flow property is the key for the study of the associated nonlocal partial differential equation (PDE). In this work we extend these studies in a non-trivial manner to mean-field SDEs which, in addition to the driving Brownian motion, are governed by a compensated Poisson random measure. We show that under suitable regularity assumptions on the coefficients of the SDE, the solution Xt,x,Pξ is twice differentiable with respect to x and its law. We establish the associated nonlocal integral-PDE, and we show that V(t,x,Pξ)=E[Φ(Xt,x,PξT,PXt,ξT)] is the unique classical solution V:[0,T]×Rd×P2(Rd)→R of this nonlocal integral-PDE with terminal condition Φ.