Recently, Multi-Contrast MR Reconstruction (MCMR) has emerged as a hot research topic that leverages high-quality auxiliary modalities to reconstruct undersampled target modalities of interest. However, existing methods often struggle to generalize across different k-space undersampling patterns, requiring the training of a separate model for each specific pattern, which limits their practical applicability. To address this challenge, we propose UniFS, a Unified Frequency-Spatial Fusion model designed to handle multiple k-space undersampling patterns for MCMR tasks without any need for retraining. UniFS integrates three key modules: a Cross-Modal Frequency Fusion module, an Adaptive Mask-Based Prompt Learning module, and a Dual-Branch Complementary Refinement module. These modules work together to extract domain-invariant features from diverse k-space undersampling patterns while dynamically adapt to their own variations. Another limitation of existing MCMR methods is their tendency to focus solely on spatial information while neglect frequency characteristics, or extract only shallow frequency features, thus failing to fully leverage complementary cross-modal frequency information. To relieve this issue, UniFS introduces an adaptive prompt-guided frequency fusion module for k-space learning, significantly enhancing the model's generalization performance. We evaluate our model on the BraTS and HCP datasets with various k-space undersampling patterns and acceleration factors, including previously unseen patterns, to comprehensively assess UniFS's generalizability. Experimental results across multiple scenarios demonstrate that UniFS achieves state-of-the-art performance. Our code is available at https://github.com/LIKP0/UniFS.