Use three languages. Before each language had his own “front page top” widget and when we changed the language it had his own widget. Now all three come out at the same time in all languages. I use WPML plugin.
Could you please specify whether there is a default widget area editor (with blocks) or a classic one that can be enabled with the Classic Widgets plugin? What if you keep 1 widget for all the languages? Does it work on the translated pages?