Deep neural network-based synthetic aperture radar (SAR) image change detection algorithms are affected by coherent speckle noise in the original image. Existing denoising methods have predominantly focused on generating binary images based on the pre-classification of original pixels, which is insufficient in removing interfering noise. Herein, to further reduce the noise points generated in the clustering algorithm, we combined the characteristics of the fuzzy clustering algorithm, demonstrating the obvious advantages of the proposed fast and flexible denoising convolutional neural network (FFDNet-F) method. An FFDNet was used to reduce noise interference in real SAR images and improve the detection accuracy and robustness of the method. Difference operators were then drawn from the weak noise images, and fuzzy local information C-means clustering was applied for analysis to generate the change detection results. The experimental results from two real datasets and the comparative analysis with other network models demonstrated the effectiveness of this method. Simultaneously, Gaofen-3 satellite images were used to verify and analyze surface flood disasters in Zhengzhou, China. The findings of this study demonstrate a significant improvement in detection accuracy using the proposed method compared with that of other algorithms.