This paper tackles the challenging problem of detecting methane plumes, a potent greenhouse gas, using Sentinel-2 imagery. This contributes to the mitigation of rapid climate change. We propose a novel deep learning solution based on U-Net with a ResNet34 encoder, integrating dual spectral enhancement techniques (Varon ratio and Sanchez regression) to optimise input features for heightened sensitivity. A key achievement is the ability to detect small plumes down to 400 m2 (i.e., for a single pixel at 20 m resolution), surpassing traditional methods limited to larger plumes. Experiments show our approach achieves a 78.39% F1-score on the validation set, demonstrating superior performance in sensitivity and precision over existing remote sensing techniques for automated methane monitoring, especially for small plumes.