Detection and tracking of tropical cyclones (TCs) in numerical weather prediction model outputs is essential for many applications, such as forecast guidance and real-time monitoring of events. While this task has been automated in the 1990s with heuristic models, relying on a set of empirical rules and thresholds, the recent success of machine learning methods to detect objects in images opens new perspectives. This paper introduces and evaluates the capacity of a convolutional neural network based on the U-Net architecture to detect the TC wind structure, including maximum wind speed area and hurricane-force wind speed area, in the outputs of the convective-scale AROME model. A dataset of 400 AROME forecasts over the West Indies domain has been entirely hand-labeled by experts, following a rigorous process to reduce heterogeneities. The U-Net performs well on a wide variety of TC intensities and shapes, with an average intersection-over-union metric of around 0.8. Its performances, however, strongly depend on the TC strength, and the detection of weak cyclones is more challenging since their structure is less well defined. The U-Net also significantly outperforms an operational heuristic detection model, with a significant gain for weak TCs, while running much faster. In the last part, the capacity of the U-Net to generalize on slightly different data is demonstrated in the context of a domain change and a resolution increase. In both cases, the pretrained U-Net achieves similar performances as the original dataset.