Current unsupervised learning approaches employ image-to-image translation networks to reduce inter-modal discrepancy before applying mono-modal registration techniques. However, significant inherent differences across imaging modalities limit GAN-based spatial domain translation methods in bridging the modality gap and result in insufficient prediction accuracy for texture-dependent registration networks. To address this, we propose a Frequency-aware and Geometric structure-guided multi-modality image Registration framework (FGR). The framework utilizes both spatial and frequency domain information for modality translation, and incorporates the proposed Texture-Structure Aware Module (T-SAM) to guide the deep registration network in extracting geometric structural features and integrating them with texture information for precise deformation prediction, thereby enabling it to excavate geometric structural features with stronger modality correlations. This design avoids purely mono-modal registration paradigms. Experimental results demonstrate that our method achieves state-of-the-art performance in multi-modality registration task.