Modern face recognition systems utilize deep neural networks to extract salient features from a face. These features denote embeddings in latent space and are often stored as templates in a face recognition system. These embeddings are susceptible to data leakage and, in some cases, can even be used to reconstruct the original face image. To prevent compromising identities, template protection schemes are commonly employed. However, these schemes may still not prevent the leakage of soft biometric information such as age, gender and race. To alleviate this issue, we propose a novel technique that combines Fully Homomorphic Encryption (FHE) with an existing template protection scheme known as PolyProtect. We show that the embeddings can be compressed and encrypted using FHE and transformed into a secure PolyProtect template using polynomial transformation, for additional protection. We demonstrate the efficacy of the proposed approach through extensive experiments on multiple datasets. Our proposed approach ensures irreversibility and unlinkability, effectively preventing the leakage of soft biometric attributes from face embeddings without compromising recognition accuracy.