Ensure the Language Tag in Joomla for your languages matches the CB language plugin. For example for French it should have fr-FR for Language Tag. I'm not sure what to suggest as this works fine in my tests. What are you using to switch languages? It's possible for CB to be loaded earlier than say Joomlas language filter plugin, which can cause this. This usually only happens with CB Auto Actions if you're acting on a very early Joomla trigger like one of the routing triggers. Are you sure your installed CB language plugin has those strings translated or is all of CB including things you're sure are translated not translating?

Unpublish the CB Auto Actions system plugin in Extensions > Plugins and see if it's a loading issue. If that doesn't fix the issue then CB isn't loading too early. CB it self does not determine what language to load. It pulls that entirely from Joomlas own API call JFactory::getLanguage()->getTag(). The only reason for CB to fail to load the matching language is the tag doesn't match that of CBs or CB was loaded too early.

Overrides have no means of forcing language loading. Sounds like you maybe had some sort of caching issue.