Accurate forecasting of three-dimensional (3D) cloud fields is important for atmospheric analysis and short-range numerical weather prediction, yet it remains challenging because cloud evolution involves cross-layer interactions, nonlocal dependencies, and multiscale spatiotemporal dynamics. Existing spatiotemporal prediction models based on convolutions, recurrence, or attention often rely on locality-biased representations and therefore struggle to preserve fine cloud structures in volumetric forecasting tasks. To address this issue, we propose QENO, a hybrid quantum-inspired spatiotemporal forecasting framework for 3D cloud fields. The proposed architecture consists of four components: a classical spatiotemporal encoder for compact latent representation, a topology-aware quantum enhancement block for modeling nonlocal couplings in latent space, a dynamic fusion temporal unit for integrating measurement-derived quantum features with recurrent memory, and a decoder for reconstructing future cloud volumes. Experiments on CMA-MESO 3D cloud fields show that QENO consistently outperforms representative baselines, including ConvLSTM, PredRNN++, Earthformer, TAU, and SimVP variants, in terms of MSE, MAE, RMSE, SSIM, and threshold-based detection metrics. In particular, QENO achieves an MSE of 0.2038, an RMSE of 0.4514, and an SSIM of 0.6291, while also maintaining a compact parameter budget. These results indicate that topology-aware hybrid quantum-classical feature modeling is a promising direction for 3D cloud structure forecasting and atmospheric Earth observation data analysis.