In intensively managed forests in Europe, where forests are divided into stands of small size and may show heterogeneity within stands, a high spatial resolution (10 - 20 meters) is arguably needed to capture the differences in canopy height. In this work, we developed a deep learning model based on multi-stream remote sensing measurements to create a high-resolution canopy height map over the "Landes de Gascogne" forest in France, a large maritime pine plantation of 13,000 km$^2$ with flat terrain and intensive management. This area is characterized by even-aged and mono-specific stands, of a typical length of a few hundred meters, harvested every 35 to 50 years. Our deep learning U-Net model uses multi-band images from Sentinel-1 and Sentinel-2 with composite time averages as input to predict tree height derived from GEDI waveforms. The evaluation is performed with external validation data from forest inventory plots and a stereo 3D reconstruction model based on Skysat imagery available at specific locations. We trained seven different U-net models based on a combination of Sentinel-1 and Sentinel-2 bands to evaluate the importance of each instrument in the dominant height retrieval. The model outputs allow us to generate a 10 m resolution canopy height map of the whole "Landes de Gascogne" forest area for 2020 with a mean absolute error of 2.02 m on the Test dataset. The best predictions were obtained using all available satellite layers from Sentinel-1 and Sentinel-2 but using only one satellite source also provided good predictions. For all validation datasets in coniferous forests, our model showed better metrics than previous canopy height models available in the same region.