Exactly, I'm using Polylang a multilanguage plugin.
I didn't realize that now my members biographic information is found in a different place.
'description' is empty and now it has several sub fields as much as languages I have assigned (e.g. 'description_fr'), that's why it couldn't never work.
Anyway the only thing if possible I would recommend to improve with hovercards plugin would be to find a way to make it react faster, just to give you an idea, with a poor machine that I use for tests, I'm getting 7 seconds until a hovercard display by hovering an avatar.