Perhaps this question is slightly out of scope for this page, but I still ask here.
Can you work for a university/academic institution as a researcher or as a teacher, with the status of a freelancer? In case this helps, I'm based in France and have applied for a freelance status (called auto-entrepreneur/micro entrepreneur in the French administrative terms), and even though I'm searching for regular temporary/permanent position in France, this hasn't seen any success yet, so I want to use that freelance status to do research at a high level (at least postdoctoral) as I strongly feel I'm genuinely passionate by fundamental research, so I've to find a way to do so, even if I may or may not be good enough to secure a formal position.
Just in case this helps: my subject(s) will be ideally the intersection between differential geometry and statistics/statistical machine learning, manifold learning, but open to other topics, e.g. applied differential geometry, or just statistical learning etc.
From my having spent long time in academia, I've never seen this happening, because normally the academic contracts are either regular CDD or CDI's. But I wonder if the above possibilities still exist in France or abroad?
EDIT: Some people asked me about my motivation for the same. It is my continued interest to do research and publish, but also to earn some money on the side by consulting or freelance jobs etc. IN fact once you're a freelance, you can hire other freelance to do your freelance projects not related to academia/research, so essentially some income without working, where I work on academic research projects myself. This is the reason I want my postdoc related contract to be a freelance once, where I can be employed as a consultant for a project.