The widespread deployment of products powered by machine learning models is raising concerns around data privacy and information security worldwide. To address this issue, Federated Learning was first proposed as a privacy-preserving alternative to conventional methods that allow multiple learning clients to share model knowledge without disclosing private data. A complementary approach known as Fully Homomorphic Encryption (FHE) is a quantum-safe cryptographic system that enables operations to be performed on encrypted weights. However, implementing mechanisms such as these in practice often comes with significant computational overhead and can expose potential security threats. Novel computing paradigms, such as analog, quantum, and specialized digital hardware, present opportunities for implementing privacy-preserving machine learning systems while enhancing security and mitigating performance loss. This work instantiates these ideas by applying the FHE scheme to a Federated Learning Neural Network architecture that integrates both classical and quantum layers.