Face super-resolution (FSR) under limited computational budgets remains challenging. Existing methods often treat all facial pixels equally, leading to suboptimal resource allocation and degraded performance. CNNs are sensitive to high-frequency facial features such as contours and outlines, while Mamba excels at capturing low-frequency attributes like facial color and texture with lower complexity than Transformers. Motivated by this, we propose FADPNet, a Frequency-Aware Dual-Path Network that decomposes facial features into low- and high-frequency components for dedicated processing. The low-frequency branch employs a Mamba-based Low-Frequency Enhancement Block (LFEB) that integrates state-space attention with squeeze-and-excitation to restore global interactions and emphasize informative channels. The high-frequency branch uses a CNN-based Deep Position-Aware Attention (DPA) module to refine structural details, followed by a lightweight High-Frequency Refinement (HFR) module for further frequency-specific refinement. These designs enable FADPNet to achieve a strong balance between FSR quality and efficiency, outperforming existing methods.