It's not a bad analogy when leavers use the UK as an example of proper democracy. By making that analogy, I'm just pointing to the fact that the system isn't that different, it's an indirect democracy where leaders with a popular mandate take decisions for us, now if I was totally honest I would say that the commissioner proposed by the french president has more legitimacy than the commissioner proposed by the UK PM since the french president is directly elected by the french electorate, in that sense we do have a problem.
But seriously I don't think that your system is bad or non democratic, it's just not that direct and you don't have as much say as some pretend even when we are talking about your head of government.