After presenting a new CCG supertagging algorithm based on morphological and dependency syntax information, we use this algorithm to create a CCG French Tree Bank corpus (20,261 sentences) based on the FTB corpus by Abeillé et al. We then use this corpus, as well as the Groningen Tree Bank corpus for the English language, to train a new BiLSTM+CRF neural architecture that uses (a) morphosyntactic input features and (b) feature correlations as input features. We show experimentally that for an inflected language like French, dependency syntax information allows significant improvement of the accuracy of the CCG supertagging task, when using deep learning techniques.