Displaying custom taxonomy menu in custom post type archive

Displaying two different menus base on the archive is no problem using is_post_type_archive()

What you are looking for is essentially the link to an term archive that only contains posts of a certain post type. Something like /index.php?term=US&post_type=pub. As far as I’m aware of WordPress doesn’t offer this natively.

You will have to create your own page template and rewrite rules to make it display like /restaurants/fr.
I think this questions covers enough about that:
How to pass URL parameters for advanced taxonomy queries with multiple terms for one custom taxonomy

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