In the modern labor market, accurate matching of job vacancies with suitable candidate CVs is critical. We present a novel multilingual knowledge graph-based framework designed to enhance the matching by accurately extracting the skills requested by a job and provided by a job seeker in a multilingual setting and aligning them via the standardized skill labels of the European Skills, Competences, Qualifications and Occupations (ESCO) taxonomy. The proposed framework employs a combination of state-of-the-art techniques to extract relevant skills from job postings and candidate experiences. These extracted skills are then filtered and mapped to the ESCO taxonomy and integrated into a multilingual knowledge graph that incorporates hierarchical relationships and cross-linguistic variations through embeddings. Our experiments demonstrate a significant improvement of the matching quality compared to the state of the art.