Fine-scale forest monitoring is essential for understanding canopy structure and its dynamics, which are key indicators of carbon stocks, biodiversity, and forest health. Deep learning is particularly effective for this task, as it integrates spectral, temporal, and spatial signals that jointly reflect the canopy structure. To address this need, we introduce THREASURE-Net, a novel end-to-end framework for Tree Height Regression And Super-Resolution. The model is trained on Sentinel-2 time series using reference height metrics derived from LiDAR HD data at multiple spatial resolutions over Metropolitan France to produce annual height maps. We evaluate three model variants, producing tree-height predictions at 2.5 m, 5 m, and 10 m resolution. THREASURE-Net does not rely on any pretrained model nor on reference very high resolution optical imagery to train its super-resolution module; instead, it learns solely from LiDAR-derived height information. Our approach outperforms existing state-of-the-art methods based on Sentinel data and is competitive with methods based on very high resolution imagery. It can be deployed to generate high-precision annual canopy-height maps, achieving mean absolute errors of 2.63 m, 2.70 m, and 2.88 m at 2.5 m, 5 m, and 10 m resolution, respectively. These results highlight the potential of THREASURE-Net for scalable and cost-effective structural monitoring of temperate forests using only freely available satellite data. The source code for THREASURE-Net is available at: https://github.com/Global-Earth-Observation/threasure-net.