As a gym owner and software developer that loves technology, including 24 hour unattended access systems, I believe that your concept would do well in certain fitness gyms, like the 24 hour access gyms that do not have round the clock employees or personal trainers (PT).
I looked up your website and it was in French so I could not see all the services it has to offer. But if it provides the ability for PTs to give members workouts tailored to their needs (when PT’s cannot be there personally or members want to lower their PT costs by seeing them less but still being accountable to someone/something), sets goals, and keeps track of their progress (weight, body fat, etc…) and/or gives members the ability to set up competitions with other “friend” members at the same gym or competing gyms…then it will do well here in the US (especially the Bay Area, CA).
Does France have a market for gym management software (GMS) or other membership tracking systems? If so, what is your (fitness gyms) primary service providers?
Just curious because I am want to expand my market outside of the US as well.
I hope this my personal Insight helps!