Although Vision Transformers based on window mechanisms have shown remarkable performance in remote sensing image super-resolution (RSISR), the traditional window mechanism limits the interaction of global information. Moreover, the large range and rich high-frequency information of remote sensing images make reconstruction more challenging. To address these issues, this paper proposes a new RSISR framework called MSFA-RSISR based on the SwinTransformer: It innovatively introduces Frequency Fourier Block (FFB) to enhance high-frequency feature extraction; designs a Multi-scale Fusion Block (MSFB) to optimize the balance between global and local features through multi-scale recursion and feature compression; and employs a three-stage training strategy from natural images to remote sensing images to efficiently integrate cross-domain knowledge. Experiments on multiple datasets demonstrate that this method significantly improves the reconstruction of high-frequency details and the recovery of global structures.