Face super-resolution (FSR) under limited computational costs remains an open problem. Existing approaches typically treat all facial pixels equally, resulting in suboptimal allocation of computational resources and degraded FSR performance. CNN is relatively sensitive to high-frequency facial features, such as component contours and facial outlines. Meanwhile, Mamba excels at capturing low-frequency features like facial color and fine-grained texture, and does so with lower complexity than Transformers. Motivated by these observations, we propose FADPNet, a Frequency-Aware Dual-Path Network that decomposes facial features into low- and high-frequency components and processes them via dedicated branches. For low-frequency regions, we introduce a Mamba-based Low-Frequency Enhancement Block (LFEB), which combines state-space attention with squeeze-and-excitation operations to extract low-frequency global interactions and emphasize informative channels. For high-frequency regions, we design a CNN-based Deep Position-Aware Attention (DPA) module to enhance spatially-dependent structural details, complemented by a lightweight High-Frequency Refinement (HFR) module that further refines frequency-specific representations. Through the above designs, our method achieves an excellent balance between FSR quality and model efficiency, outperforming existing approaches.