Forward-looking sonar (FLS) images present various challenges in interpretation, recognition, and segmentation due to limitations like low resolution, speckle noise, and low contrast, making them more complex than optical images. Existing methods often focus solely on denoising or enhancement, neglecting the potential benefits of utilizing multi-scale features to create an integrated image processing approach. This paper introduces the Laplacian pyramid-based Multi-scale Denoising and Enhancement (LPMsDE) method tailored for FLS images. The proposed method begins by presenting a novel multiplicative speckle noise model, grounded in the Gaussian distribution, specifically designed for FLS images. Next, the Laplacian pyramid decomposition is utilized to estimate noise variance, with an improved adaptive local filter. Lastly, a combination of the Laplacian pyramid framework, the enhanced adaptive local filter, and Contrast-Limited Histogram Equalization (CLHE) is employed to denoise and enhance images at different resolution levels. Through comprehensive experiments conducted on both simulated and real sonar images, the effectiveness of the LPMsDE method is demonstrated. It surpasses other denoising and enhancement techniques, as evidenced by superior scores in Structural Similarity Index (SSIM), Peak Signal-to-Noise Ratio (PSNR), Equivalent Number of Looks (ENL), Natural Image Quality Evaluator (NIQE), and Blind/Referenceless Image Spatial Quality Evaluator (BRISQUE).