Algorithmic recommendations of job ads have the potential to reduce frictional unemployment, but raise concerns about fairness due to biases in past data. Our research investigates the issue of algorithmic fairness with a specific focus on gender in a hybrid job recommendation system developed in partnership with the French Public Employment Service (PES), which is trained on past hires. First, by viewing job ads as a set of characteristics (such as wage and contract type), we document how the algorithm treats job seekers differently based on gender, both unconditionally and conditionally on their search parameters and qualifications. Second, we discuss the notion(s) of algorithmic fairness applicable in this context and the trade-offs involved. We show that the considered system reflects some existing differences in hiring or applications but does not exacerbate them. Finally, we consider adversarial de-biasing technique as a practical tool to demonstrate the trade-offs between recall and reduced differentiated treatment.