Methane is a powerful greenhouse gas that contributes significantly to global warming. Accurate detection of methane emissions is the key to taking timely action and minimizing their impact on climate change. We present AttMetNet, a novel attention-enhanced deep learning framework for methane plume detection with Sentinel-2 satellite imagery. The major challenge in developing a methane detection model is to accurately identify methane plumes from Sentinel-2's B11 and B12 bands while suppressing false positives caused by background variability and diverse land cover types. Traditional detection methods typically depend on the differences or ratios between these bands when comparing the scenes with and without plumes. However, these methods often require verification by a domain expert because they generate numerous false positives. Recent deep learning methods make some improvements using CNN-based architectures, but lack mechanisms to prioritize methane-specific features. AttMetNet introduces a methane-aware architecture that fuses the Normalized Difference Methane Index (NDMI) with an attention-enhanced U-Net. By jointly exploiting NDMI's plume-sensitive cues and attention-driven feature selection, AttMetNet selectively amplifies methane absorption features while suppressing background noise. This integration establishes a first-of-its-kind architecture tailored for robust methane plume detection in real satellite imagery. Additionally, we employ focal loss to address the severe class imbalance arising from both limited positive plume samples and sparse plume pixels within imagery. Furthermore, AttMetNet is trained on the real methane plume dataset, making it more robust to practical scenarios. Extensive experiments show that AttMetNet surpasses recent methods in methane plume detection with a lower false positive rate, better precision recall balance, and higher IoU.