This paper investigates cross-layer design for differentially private federated learning over cell-free massive MIMO networks with over-the-air (OTA) aggregation. Distributed access points (APs) collaboratively serve user equipments (UEs) through user-centric clustering, where clipped local model updates are perturbed with Gaussian noise and simultaneously transmitted over a shared uplink for OTA averaging at a central processing unit. Exploiting channel hardening, we show that thermal noise inherent in wireless reception can act as a privacy-masking resource, reducing or even eliminating the need for artificial noise. Based on this observation, we formulate a joint optimization problem over AP-UE associations, UE transmit powers, and artificial noise variances to minimize aggregation variance subject to per-UE zero-concentrated differential privacy constraints derived from an ergodic privacy accounting framework. Analysis reveals a regime-dependent structure: stringent privacy requirements favor low transmit powers and sparse AP associations to exploit thermal noise for privacy, whereas relaxed requirements favor larger clusters to improve aggregation quality. The resulting mixed-integer nonconvex problem is solved via alternating optimization combining difference-of-convex power allocation and greedy coordinate-descent clustering. Numerical results show up to 89% lower aggregation variance than conventional baselines and enable 97% test accuracy on MNIST with consistent gains on CIFAR-10. Under strict privacy budgets, competing schemes remain near random-chance performance, while under relaxed budgets they continue to lag significantly behind the proposed design.

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