This paper introduces a quantum-inspired denoising framework that integrates the Quantum Fourier Transform (QFT) into classical audio enhancement pipelines. Unlike conventional Fast Fourier Transform (FFT) based methods, QFT provides a unitary transformation with global phase coherence and energy preservation, enabling improved discrimination between speech and noise. The proposed approach replaces FFT in Wiener and spectral subtraction filters with a QFT operator, ensuring consistent hyperparameter settings for fair comparison. Experiments on clean speech, synthetic tones, and noisy mixtures across diverse signal to noise ratio (SNR) conditions, demonstrate statistically significant gains in SNR, with up to 15 dB improvement and reduced artifact generation. Results confirm that QFT based denoising offers robustness under low SNR and nonstationary noise scenarios without additional computational overhead, highlighting its potential as a scalable pathway toward quantum-enhanced speech processing.