The issue would appear to be that you do not have to reside in France to undertake a distance learning course. The whole point about distance learning really. I see nothing ridiculous in not granting residence to someone studying via distance learning. You should consider why you have now enrolled via distance learning when (presumably) you were successfully resident as a student for your previous study.
1) You could try a written response that your residence is only for the period of the stage, and ask for a review of the decision based on a fresh application for a short term study permit.
2) You could ask GE to support a short term work permit.