The U-Net model and its variants have been extensively employed in medical image segmentation tasks, particularly with the incorporation of advanced modules such as the Transformer. However, these methods continue to encounter challenges in effectively capturing both local and global information. To optimize the utilization of local and global image data while maintaining minimal computational complexity, this paper proposes the F2Unet (Fourier-Enhanced F-shaped U-Net) model. This model integrates the principles of the Fourier transform with those of the conventional U-Net model. Specifically, two distinct methods of combining convolution and attention mechanisms are utilized to complement each other during the down-sampling stage. Various combinations of Fourier transform and convolution are employed to capture both local and global information during the up-sampling stage. Additionally, depth-separable convolution is implemented to achieve feature fusion between high-dimensional and low-dimensional images in the skip-connection stage. Although the proposed model exhibits a slight increase in computational complexity compared to the original segmentation model, experimental results on four public datasets indicate that F2Unet demonstrates a significant advantage in terms of segmentation performance when compared to other U-Net variants and advanced segmentation methods.