Aligning language models with human values is crucial, especially as they become more integrated into everyday life. While models are often adapted to user preferences, it is equally important to ensure they align with moral norms and behaviours in real-world social situations. Despite significant progress in languages like English and Chinese, French has seen little attention in this area, leaving a gap in understanding how LLMs handle moral reasoning in this language. To address this gap, we introduce Histoires Morales, a French dataset derived from Moral Stories, created through translation and subsequently refined with the assistance of native speakers to guarantee grammatical accuracy and adaptation to the French cultural context. We also rely on annotations of the moral values within the dataset to ensure their alignment with French norms. Histoires Morales covers a wide range of social situations, including differences in tipping practices, expressions of honesty in relationships, and responsibilities toward animals. To foster future research, we also conduct preliminary experiments on the alignment of multilingual models on French and English data and the robustness of the alignment. We find that while LLMs are generally aligned with human moral norms by default, they can be easily influenced with user-preference optimization for both moral and immoral data.