Bidirectional Encoder Representations from Transformers (BERT) and its related variants have a new state-of-the-art performance in the natural language processing domain. Recently, SBERT has transformed the use of BERT, in order to reduce the computational effort of sentence similarity, while maintaining the accuracy of BERT. However, these models have been trained on non-specific texts of a given language, which does not allow for a fine-grained representation of texts from specific domains, such as the French medical domain. In this paper, we present F-BERTMed, a French sentence embedding framework based on FlauBERT, whose pre-training using MLM (Masked Language Modeling) has been extended on French medical texts, before being fine-tuned on NLI (Natural Language Inference) and STS (Semantic Textual Similarity) tasks. The performance evaluation of F-BERTMed on STS tasks, as well as on classification tasks, confirmed that the proposed methodology has significant advantages over other state-of-the-art methods.