With the widespread application of facial image data across various domains, the efficient storage and transmission of facial images has garnered significant attention. However, the existing learned face image compression methods often produce unsatisfactory reconstructed image quality at low bit rates. Simply adapting diffusion-based compression methods to facial compression tasks results in reconstructed images that perform poorly in downstream applications due to insufficient preservation of high-frequency information. To further explore the diffusion prior in facial image compression, we propose Facial Image Compression with a Stable Diffusion Prior (FaSDiff), a method that preserves consistency through frequency enhancement. FaSDiff employs a high-frequency-sensitive compressor in an end-to-end framework to capture fine image details and produce robust visual prompts. Additionally, we introduce a hybrid low-frequency enhancement module that disentangles low-frequency facial semantics and stably modulates the diffusion prior alongside visual prompts. The proposed modules allow FaSDiff to leverage diffusion priors for superior human visual perception while minimizing performance loss in machine vision due to semantic inconsistency. Extensive experiments show that FaSDiff outperforms state-of-the-art methods in balancing human visual quality and machine vision accuracy. The code will be released after the paper is accepted.