Stereo Image Super-Resolution (stereoSR) has attracted significant attention in recent years due to the extensive deployment of dual cameras in mobile phones, autonomous vehicles and robots. In this work, we propose a new StereoSR method, named SwinFSR, based on an extension of SwinIR, originally designed for single image restoration, and the frequency domain knowledge obtained by the Fast Fourier Convolution (FFC). Specifically, to effectively gather global information, we modify the Residual Swin Transformer blocks (RSTBs) in SwinIR by explicitly incorporating the frequency domain knowledge using the FFC and employing the resulting residual Swin Fourier Transformer blocks (RSFTBs) for feature extraction. Besides, for the efficient and accurate fusion of stereo views, we propose a new cross-attention module referred to as RCAM, which achieves highly competitive performance while requiring less computational cost than the state-of-the-art cross-attention modules. Extensive experimental results and ablation studies demonstrate the effectiveness and efficiency of our proposed SwinFSR.