Canopy height is a key indicator of tropical forest structure. In this study, we present a deep learning application to map canopy height in French Guiana using freely available multi-source satellite data (optical and radar) and complementary environmental information. The potential of a U-Net architecture trained on sparse and unevenly distributed GEDI data to generate a continuous canopy height map at a regional scale was assessed. The developed model, named CHNET, successfully produced a canopy height map of French Guiana at a 10-m spatial resolution, achieving relatively good accuracy compared to a validation airborne LiDAR scanning (ALS) dataset. The study demonstrates that relevant environmental descriptors, namely, height above nearest drainage (HAND) and forest landscape types (FLT), significantly contribute to the model's accuracy, highlighting that these descriptors bring important information on canopy structural properties and that the CHNET framework can efficiently use this information to improve canopy height prediction. Another critical aspect highlighted is the necessity of addressing GEDI data inaccuracies and geolocation uncertainties, which is essential for any GEDI-based application. However, challenges remain, particularly in characterizing tall canopies, as our CHNET model exhibits a tendency to underestimate canopy heights greater than 35 m. A large part of this error arises from the use of GEDI measurements as reference, given the fact these data exhibit certain saturation in tropical biomes. Future improvements in the analysis of GEDI signal as well as the implementation of robust models are essential for better characterization of dense and tall tropical forest ecosystems.