I think you understand you exactly. This is an EMBA for outsiders. The whole point of HEC's grande ecole programme is that it's for insiders. You work like a dog to get through the prepa, and then HEC is where you network, drink wine, play rugby, network and build leadership and soft skills. But in *this* EMBA there will be some rough diamonds: people who are not successful enough in their current role to be supported through the EMBA or to want to stay in their current role and industry. This could be a volatile group, with a lot of highs and lows. I spent a year in the EMBA at EDHEC, in comparison, and this was a very stable group of senior managers, I think just one of these 'outsider' types. I feel I learnt a lot about managerial success from my classmates, and part of the reason I moved to the EMBA at LBS was that I saw the quality of the classmates was a key thing for me, alongside the pedagogy.
If I was in Paris, I would look at the EMBA or the executive MSc SMIB at ESSEC, and I would look at the Paris campuses of EMLyon, ESCP Europe, Neoma and EDHEC.
PS The dual EMBAs at ESSEC and ENPC are impressive:
https://pontsbschool.com/programs/global-executive-mba/program-highlights/http://www.essec-mannheim.com/