This article presents MedDialog-FR, a large publicly available corpus of French medical conversations for the medical domain. Motivated by the lack of French dialogue corpora for data-driven dialogue systems and the paucity of available information related to women's intimate health, we introduce an annotated corpus of question-and-answer dialogues between a real patient and a real doctor concerning women's intimate health. The corpus is composed of about 20,000 dialogues automatically translated from the English version of MedDialog-EN. The corpus test set is composed of 1,400 dialogues that have been manually post-edited and annotated with 22 categories from the UMLS ontology. We also fine-tuned state-of-the-art reference models to automatically perform multi-label classification and response generation to give an initial performance benchmark and highlight the difficulty of the tasks.