Indeed, for the hospital it's probably part of the story: directors are now not required to have been doctors before.

Maybe having pairs (one doctor, one non doctor) for those jobs would be a solution.

But it's probably not the only problem.

France has a budget problem, it's been borrowing more and more, and producing less and less. We can't maintain our way of life without cutting some spending, and you do it where people complain less, or where consequences will be seen way down the road.