In this paper we address the problem of modal sense classification for the French modal verb pouvoir in a transcribed spoken corpus. To the best of our knowledge, no studies have focused on this task in French. We fine-tuned various BERT-based models for French in order to determine which one performed best. It was found that the Flaubert-base-cased model was the most effective (F1-score of 0.94) and that the most frequent categories in our corpus were material possibility and ability, which are both part of the more global alethic category.