CB lists and profiles in multilingual site

I thought there was a way without duplicating menu items.

There is if you don't care about translating the menu alias (the part shown in the address bar of your browser). The menu title and module title should be translatable using Joomla language overrides and custom language keys. If the overrides don't work for translating those then yes you'll have to create duplicates.

There is if you don't care about translating the menu alias (the part shown in the address bar of your browser).

You forgot to mention the multilanguage hreflang and alternate tags, which are also very important for SEO (if I'm not mistaken here...)

Now I understand more how to make the translations, I also read all the tutorials about that + watch the videos, but one thing I cannot translate: the CB Login module title.
As you recommended, I left only one module CB Login for all languages but next I've tried to enter in CB's language plugins overrides tab this: (for french)
and also this: (as a parameter translation override)

None of them makes the translation.
What am I doing wrong?

CB is not responsible for parsing and displaying the module title. Joomla handles that. So you have to use Joomla language overrides to translate the module title if Joomla even allows that.