Pre-print, Working paper: In this paper, we propose a job assignment model allowing for a gender difference in access to jobs. Males and females compete for the same job positions. They are primarily interested in the best-paid jobs. A structural relationship of the model can be used to empirically recover the probability ratio of females and males getting a given job position. As this ratio is allowed to vary with the rank of jobs in the wage distribution of positions, barriers in females' access to high-paid jobs can be detected and quantiffed. We estimate the gender relative probability of getting any given job position for full-time executives aged 40-45 in the private sector. This is done using an exhaustive French administrative dataset on wage bills. Our results show that the access to any job position is lower for females than for males. Also, females' access decreases with the rank of job positions in the wage distribution, which is consistent with females being faced with more barriers to high-paid jobs than to low-paid jobs. At the bottom of the wage distribution, the probability of females getting a job is 12% lower than the probability of males. The difference in probability is far larger at the top of the wage distribution and climbs to 50%.