With the increasing deployment of facial image data across a wide range of applications, efficient compression tailored to facial semantics has become critical for both storage and transmission. While recent learning-based face image compression methods have achieved promising results, they often suffer from degraded reconstruction quality at low bit rates. Directly applying diffusion-based generative priors to this task leads to suboptimal performance in downstream machine vision tasks, primarily due to poor preservation of high-frequency details. In this work, we propose FaSDiff (\textbf{Fa}cial Image Compression with a \textbf{S}table \textbf{Diff}usion Prior), a novel diffusion-driven compression framework designed to enhance both visual fidelity and semantic consistency. FaSDiff incorporates a high-frequency-sensitive compressor to capture fine-grained details and generate robust visual prompts for guiding the diffusion model. To address low-frequency degradation, we further introduce a hybrid low-frequency enhancement module that disentangles and preserves semantic structures, enabling stable modulation of the diffusion prior during reconstruction. By jointly optimizing perceptual quality and semantic preservation, FaSDiff effectively balances human visual fidelity and machine vision accuracy. Extensive experiments demonstrate that FaSDiff outperforms state-of-the-art methods in both perceptual metrics and downstream task performance.