Hello Chouby,
yes it is claimed as fully translatable with WPML, and until recently it was almost ok : It's the 'adapt' theme (premium version) from wpexplorer, so 'almost' means excepted a few strings (custom headers)from Option Framework incorporated to the theme. That issue was already discussed here : http://wordpress.org/support/topic/polyland-and-latest-pytheas-theme?replies=27 but nothing more. As the theme admin displays a 'Slightly Modified Options Framework 1.5.2' I guess the hand update to smof 1.6 would correct that too... (I discuss the issue with the creator of the theme, he said he would soon move all his theme to 'theme customizer' anyway, for anybody's information)
But I don't think my specific issue is related (which as no value as a clue). Plus : excepted if I always has been lucky while checking the website along two months, I really think it was working perfectly until recently.. which gives the bad feeling that something degenerated along time.
To describe the issue as simply as possible, the custom post type is made of 'title' 'content' 'URL' (slug too of course), and while title or content are independant for the two languages, URL value became unique, or synchronized, between translations.
it looks like that : http://studio.neq3.com/imageshare