This paper investigates tree species classification using Sentinel-2 multispectral satellite image time-series. Despite their critical importance for many applications, such maps are often unavailable, outdated, or inaccurate for large areas. The interest of using remote sensing time series to produce these maps has been highlighted in many studies. However, many methods proposed in the literature still rely on a standard classification algorithm, usually the Random Forest (RF) algorithm with vegetation indices. This study shows that the use of deep learning models can lead to a significant improvement in classification results, especially in an imbalanced context where the RF algorithm tends to predict towards the majority class. In our use case in the center of France with 10 tree species, we obtain an overall accuracy (OA) around 95% and a F1-macro score around 80% using three different benchmark deep learning architectures. In contrast, using the RF algorithm yields an OA of 93% and an F1 of 60%, indicating that the minority classes are not classified with sufficient accuracy. Therefore, the proposed framework is a strong baseline that can be easily implemented in most scenarios, even with a limited amount of reference data. Our results highlight that standard multilayer perceptron can be competitive with batch normalization and a sufficient amount of parameters. Other architectures (convolutional or attention-based) can also achieve strong results when tuned properly. Furthermore, our results show that DL models are naturally robust to imbalanced data, although similar results can be obtained using dedicated techniques.