I've finished my PhD in pure mathematics in late 2013 in the US (2 published papers, 1 preprint), and after almost 4 years of postdoc in the subjects of pure math (1 year-unproductive), medical imaging and computer vision (3 years- 3 papers), I'm joining a research position in industry in France. I've done 3 years of postdoc in France (and currently here) and 1 in the US.
I'll be working alongside a professor of statistics in France who's a consultant for my company, and the company also encourages publications (after they get patent etc.). Besides, I'm collaborating with two people from academia and industry, and in 2-3 years or so, I hope to have 2-3 more publications.
My goal is to defend my habilitation in statistics/machine learning (https://en.wikipedia.org/wiki/Habilitation) in 3-4 years from now, as I'm very interested to have a joint academic-industrial position in the future. To elaborate, I'd like to hold a professor position in academia and also a researcher/research consultant position in industry. I'm happy to indirectly supervise PhD students alongside someone else but not directly. And somewhat shamelessly, I'd like to have a second income from academia on top of industry. I'm not a EU or US citizen, by the way.
My question is: is it possible for me to defend my habilitation in France when I'm not a part of French academia? Normally, I've seen only academics do that.
Thanks in advance!