Electrocardiography (ECG) is a promising approach for continuous fetal heart rate monitoring. Its morphology can provide information on fetal health to guide patient care by clinicians. However, fetal ECGs extracted from abdominal ECGs are often too weak to reliably detect fetal heart rate. This study evaluates the application of a U-Net architecture for accurate R-peak detection in low-SNR fetal ECG signals. The proposed method achieves high accuracy with a positive predictive value of 99.81%, sensitivity of 100.00%, and an F1-score of 99.91% on direct fetal ECG from the Abdominal and Direct ECG Database, with significantly reduced false predictions, and outperforming two other baseline methods compared with. Notably, our approach demonstrates robustness, accurately predicting peaks in regions of high distortion, a capability unmatched by other methods evaluated. This finding indicates the suitability and benefits of the U-Net architecture for peak detection in fetal ECG signals.