<p>In this paper, we investigate a class of progressive optimal control problems for fully coupled mean-field forward-backward systems with random jumps. Under weakly-coupled conditions and an arbitrary fixed time horizon, we establish the well-posedness of a class of fully coupled mean-field forward-backward stochastic differential equations with jumps, ensuring the well-posedness of the state, variational and adjoint equations. Next, using the convex variational method, we provide a stochastic maximum principle for the progressive optimal control of this mean-field system. Our maximum principle is divided into two parts: a continuous component, which characterizes the optimal control during continuous periods, and a jump component, which defines the optimal control behavior at jump times. Additionally, we provide a sufficient maximum principle under certain convexity assumptions. Finally, we apply these theoretical results to a linear-quadratic control problem, obtaining both the open-loop optimal control and its corresponding feedback representation, further demonstrating the practical effectiveness of our findings.</p>