The biomedical domain has sparked a significant interest in the field of Natural Language Processing (NLP), which has seen substantial advancements with pre-trained language models (PLMs). However, comparing these models has proven challenging due to variations in evaluation protocols across different models. A fair solution is to aggregate diverse downstream tasks into a benchmark, allowing for the assessment of intrinsic PLMs qualities from various perspectives. Although still limited to few languages, this initiative has been undertaken in the biomedical field, notably English and Chinese. This limitation hampers the evaluation of the latest French biomedical models, as they are either assessed on a minimal number of tasks with non-standardized protocols or evaluated using general downstream tasks. To bridge this research gap and account for the unique sensitivities of French, we present the first-ever publicly available French biomedical language understanding benchmark called DrBenchmark. It encompasses 20 diversified tasks, including named-entity recognition, part-of-speech tagging, question-answering, semantic textual similarity, and classification. We evaluate 8 state-of-the-art pre-trained masked language models (MLMs) on general and biomedical-specific data, as well as English specific MLMs to assess their cross-lingual capabilities. Our experiments reveal that no single model excels across all tasks, while generalist models are sometimes still competitive.