This paper reports results on grammatical induction for French. We investigate how to best train a parser on the French Treebank We compare, for French, a supervised lexicalized parsing algorithm with a semi-supervised unlexicalized algorithm We report the best results known to us on French statistical parsing, that we obtained with the semi-supervised learning algorithm. The reported experiments can give insights for the task of grammatical learning for a morphologically-rich language, with a relatively limited amount of training data, annotated with a rather flat structure.