Cross-modal person re-identification aims to achieve accurate identity matching through cross-modal data (e.g., visible and infrared images), holding significant application value in intelligent security systems. However, existing methods predominantly rely on dual-stream networks to extract spatial domain features while inadequately exploring frequency domain information, making it challenging to effectively mitigate feature distribution shifts caused by modality discrepancies. This paper proposes a Frequency-Spatial Dual-Stream Fusion Network (FSFN) that enhances cross-modal matching performance by exploring modality-invariant feature representations in the frequency domain. Specifically, spatial features of visible and infrared modalities are first extracted through dual-stream network branches, while Fast Fourier Transform (FFT) is introduced to decompose images into amplitude and phase spectra. Subsequently, an attention-based feature fusion module is designed to enhance cross-modal feature consistency using structural information embedded in phase components, achieving complementary optimization of spatial-frequency features. Experiments demonstrate that on SYSU-MM01 and RegDB datasets, the proposed method achieves Rank-1/mAP accuracies of 66.01%/63.41% and 87.12%/79.97%, respectively, showing significant improvements over baseline approaches. This study provides a novel frequency-domain perspective for cross-modal feature learning.