This paper presents a job recommendation algorithm designed and validated in the context of the French Public Employment Service. The challenges, owing to the confidential data policy, are related with the extreme sparsity of the interaction matrix and the mandatory scalability of the algorithm, aimed to deliver recommendations to millions of job seekers in quasi real-time, considering hundreds of thousands of job ads. The experimental validation of the approach shows similar or better performances than the state of the art in terms of recall, with a gain in inference time of 2 orders of magnitude. The study includes some fairness analysis of the recommendation algorithm. The gender-related gap is shown to be statistically similar in the true data and in the counter-factual data built from the recommendations.