Hyperspectral and multispectral image fusion (HMIF) aims to reconstruct high-resolution hyperspectral images by integrating the spectral richness of low-resolution HSIs with the spatial structures of high-resolution MSIs. While supervised methods achieve high fusion accuracy, they are inherently limited by the practical difficulty of acquiring ground-truth labels. Existing unsupervised approaches, though more suitable for real-world scenarios, often yield suboptimal performance due to the neglect of explicit high-frequency texture reconstruction. To address this issue, we propose the Unsupervised Frequency-Guided Network (UFGNet), which eliminates label dependency while effectively restoring fine texture details. Specifically, a Quick Initial Estimation Module (QIEM) is first utilized to perform truncated singular value decomposition for extracting low-rank spectral bases, supplemented by learnable components to enhance feature representation. Subsequently, the Frequency-Guided Module (FGM) leverages Fourier transforms to map features into the frequency domain for multi-dimensional feature enhancement and noise suppression. Furthermore, a Cross-Complementary Refinement Module (CCRM) is introduced to perform cascaded spatial and spectral residual optimization for high-fidelity image fusion. A Frequency Consistency Loss is designed to guide the learning of frequency-domain priors and enforce strict constraints on the spectral-spatial reconstruction process. Experiments on the Pavia University, CAVE, and Botswana datasets at 8× super-resolution demonstrate that UFGNet improves PSNR by 2.122 dB, 3.424 dB, and 1.053 dB over twelve SOTA methods, respectively, validating the effectiveness of the proposed approach.