Deep Neural Networks (DNNs) often struggle to suppress noise at low signal-to-noise ratios (SNRs). This paper addresses speech enhancement in scenarios dominated by harmonic noise and proposes a framework that integrates cyclostationarity-aware preprocessing with lightweight DNN-based denoising. A cyclic minimum power distortionless response (cMPDR) spectral beamformer is used as a preprocessing block. It exploits the spectral correlations of cyclostationary noise to suppress harmonic components prior to learning-based enhancement and does not require modifications to the DNN architecture. The proposed pipeline is evaluated in a single-channel setting using two DNN architectures: a simple and lightweight convolutional recurrent neural network (CRNN), and a state-of-the-art model, namely ultra-low complexity network (ULCNet). Experiments on synthetic data and real-world recordings dominated by rotating machinery noise demonstrate consistent improvements over end-to-end DNN baselines, particularly at low SNRs. Remarkably, a parameter-efficient CRNN with cMPDR preprocessing surpasses the performance of the larger ULCNet operating on raw or Wiener-filtered inputs. These results indicate that explicitly incorporating cyclostationarity as a signal prior is more effective than increasing model capacity alone for suppressing harmonic interference.