Thanks to the rise of self-supervised learning, automatic speech recognition (ASR) systems now achieve near-human performance on a wide variety of datasets. However, they still lack generalization capability and are not robust to domain shifts like accent variations. In this work, we use speech audio representing four different French accents to create fine-tuning datasets that improve the robustness of pre-trained ASR models. By incorporating various accents in the training set, we obtain both in-domain and out-of-domain improvements. Our numerical experiments show that we can reduce error rates by up to 25% (relative) on African and Belgian accents compared to single-domain training while keeping a good performance on standard French.