Highly sensitive standoff methane detection is vital for atmospheric science, environmental protection, and production safety. We develop a mid-infrared methane standoff sensor using a cooperative target based on tunable diode laser absorption spectroscopy (TDLAS). To enhance sensor sensitivity, we propose a one-dimensional frequency channel attention-based convolutional neural network (1D-FCACNN) filter, which can effectively denoise the methane absorbance signals and its second harmonic signals. The filter model is adequately trained on a simulated spectrum dataset, which we constructed based on data augmentation. In comparison with reported filtering algorithms, the proposed filter shows the best performance in both measuring modes and evaluation metrics. Real-time measurements show that the measuring accuracy and limit of detection (LOD) of the proposed sensor reach a minimum of 30.40 ppb and 5.04 ppb over a 10-meter optical range, a significant improvement compared to previous reports of methane standoff sensors. The proposed methane standoff sensor proves the feasibility of enhancing the performance of TDLAS gas sensors with the attention mechanism, bringing a new option for high-sensitivity measurements of methane and other atmospheric trace gases.