Tools must be developed to help draft, consult, and explore textual legal sources. Between statistical information retrieval and the formalization of textual rules for automated legal reasoning, we defend a more pragmatic third way that enriches legal texts with a coarse-grained, interpretation-neutral, semantic annotation layer. The aim is that legal texts can be enriched on a large scale at a reasonable cost, paving the way for new search capabilities that will facilitate mining of legal sources. This new approach is illustrated on a proof-of-concept experiment that consisted in semantically annotating a significant part of the French version of the GDPR. The paper presents the design methodology of the annotation language, a first version of a Core Legal Annotation Language (CLAL), together with its formalization in XML, the gold standard resulting from the annotation of GDPR, and examples of user questions that can be better answered by semantic than by plain text search. This experimentation demonstrates the potential of the proposed approach and provides a basis for further development. All resources developed for that GDPR experiment are language independent and are publicly available.