Hi,
it was my first idea, but then I have to assign it to every single page, post or product that I create.
This site has more the 100 product The final user can’t be able and has no time to set a different header.
Then it could create more problem with WPML (menu/language widget etc).
You tested tested the site disabling plugin. So the issue should be solved inside Woodmart and WPML (that is a Woodmart partner).
I suggest you to explore this issue with WPML.
Thanks