[Решено] Custom Post Type Archive pages only pulling in EN posts on other languages

Background of the issue:
I am trying to pull in the relevant custom posts into their archive pages, but it is pulling the EN posts into other languages. Link to a page where the issue can be seen: скрытая ссылка

Symptoms:
The French posts are not displaying; instead, English posts are being shown.

Questions:
Why are English posts appearing on the French archive page?
How can I ensure the correct language posts are displayed on their respective archive pages?