Categorial grammar (CG) is a lexicalized grammar formalism that can be used to identify and extract the semantics of natural language sentences. However, despite being used actively to solve natural language understanding tasks such as natural language inference or recognizing textual entailment, most of the tools exploiting the capacities of CG are available in a limited set of languages. This paper proposes a first step toward developing a set of tools enabling the use of CG for the French language by proposing a neural network tailored for part-of-speech and type-logical-grammar supertagging, located at the frontier between computational linguistics and artificial intelligence. Experiments show that our model can compete with state-of-the art models while retaining a simple architecture.