We propose a hybrid quantum-classical algorithm for ground state energy (GSE) estimation that remains robust to highly noisy data and exhibits low sensitivity to hyperparameter tuning. Our approach -- Fourier Denoising Observable Dynamic Mode Decomposition (FDODMD) -- combines Fourier-based denoising thresholding to suppress spurious noise modes with observable dynamic mode decomposition (ODMD), a quantum-classical signal subspace method. By applying ODMD to an ensemble of denoised time-domain trajectories, FDODMD reliably estimates the system's eigenfrequencies. We also provide an error analysis of FDODMD. Numerical experiments on molecular systems demonstrate that FDODMD achieves convergence in high-noise regimes inaccessible to baseline methods under a limited quantum computational budget, while accelerating spectral estimation in intermediate-noise regimes. Importantly, this performance gain is entirely classical, requiring no additional quantum overhead and significantly reducing overall quantum resource demands.