Howdy !
Sorry for the delay, I saw your message earlier this week but didn’t had time to give it a try until today.
So I don’t think that my host (1&1) uses ModSecurity (not that I’m aware of) and I double check : all my websites have the same access authorizations (Read write execute…)
So I reinstalled Pro, but without any noticeable effects.
However I realized that this website is the only of mine which has Polylang installed. And disabling it does fix the problem. Now why it didn’t last week when I disable all plugins ? Is it today’s Polylang update (Version 2.6.5) that changes something ? …
Long story short, I’m good, I can work with polylang temporarily disable.
But voila, this way you know as well ! 
Thanks for your help !