Named entity recognition as it is traditionally envisioned excludes in practice a significant part of the entities of potential interest for real-word applications: nested, discontinuous, non-named entities. Despite various attempts to broaden their coverage, subsequent annotation schemes have achieved little adoption in the literature and the most restrictive variant of NER remains the default. This is partly due to the complexity of those annotations and their format. In this paper, we introduce a new annotation scheme that offers higher comprehensiveness while preserving simplicity, together with an annotation tool to implement that scheme. We also release the corpus UkraiNER, comprised of 10,000 French sentences in the geopolitical news domain and manually annotated with comprehensive entity recognition. Our baseline experiments on UkraiNER provide a first point of comparison to facilitate future research (82 F1 for comprehensive entity recognition, 87 F1 when focusing on traditional nested NER), as well as various insights on the composition and challenges that this corpus presents for state-of-the-art named entity recognition models.