When I “add” a product to cart, the popup, in any language I have chosen, “shopping card open message” is always in English and every link drives me to the English version of the site.
When I open the cart from the dropdown menu, it’s in the language I prefer.

Normally, the modal popup is translated by Virtuemart Core package using these text syntax:

COM_VIRTUEMART_CART_OVERVIEW
COM_VIRTUEMART_CART_PRODUCT_ADDED
COM_VIRTUEMART_CONTINUE_SHOPPING
COM_VIRTUEMART_CART_SHOW

So, once you successfully translate the Virtuemart, then modal should also be translated just fine.

ARe you working on a live website? What is your website URL where i can check to see what is going on.

Regards