Link between custom Post Type – switcher lang – archives page

Hello,
I’m having a slight problem with the link between the FR and EN versions for a custom content type.
On the “slides” page (custom post type), I can click on the “UK” flag, the EN version is correctly loaded, but being on the EN version, when I click on the “FR” flag, the link takes me back to the EN home page.
Would you have any idea how to correct this problem? The two menu links load “Publication type archive”.

The page I need help with: [log in to see the link]