Future wireless networks aim to deliver ultra-reliable and low-latency services while containing their rapidly growing energy footprint. In a cell-free radio access network (CF-RAN), this objective translates into a tightly coupled optimisation over access point (AP) activation, user association, precoding design and virtual-CPU provisioning, all under finite-blocklength reliability constraints. We build a detailed power model that includes radio hardware, fronthaul and load-dependent computing, then recast the resulting energy efficiency problem as a mixed-integer second-order cone programming using a tight surrogate for decoding-error probability. A sparsity-promoting convex–concave solver can reach near-optimal solutions but must be run for every channel realisation, making real-time use impractical. To overcome this limitation, we propose a graph neural network (GNN) that represents CF-RAN as a heterogeneous AP-to-user graph, predicts precoding vectors, rates and soft association probabilities in a single forward pass, and then applies a lightweight reliability-enforcement layer to remove any residual violations. Simulation results show that, whenever the constraints are feasible, the learned solver achieves comparable energy efficiency as the optimization-based baseline while operating with only a single-pass inference step per channel realization.