I have been living as a student in Paris since Oct 17, 2010. My student permit expired on Dec 31, 2011. This morning I had my appointment to apply for extension. I am currently doing a stage until May 6, 2012 as I enrolled in CNFDI to do a program by distance called "expression ecrite". I got the Convention du Stage from them and GE Healthcare also signed it. This morning the prefecture told me that the school I am in does not count because it is by distance and they rejected my application. They told me I will receive a letter in 3 weeks telling me what my options are.
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.