Hi @yann,
I’m extremely sorry.
I looked at this and played with polylang. It looks like the way how polylang associates the posts with a language is something cannot be done using GIW.
You can however create posts using GIW in whatever organization you want, but to let polylang know what post is associated to which language cannot be done.
As of now GIW does not have any official integration with polylang. This is not in the todo list. Not sure how long it would take.
I would suggest to use GIW only for one posts of one language.
Thanks,
Aakash