At the moment the request to the cart.js doesn't fetch the translated content of the products such as the title.
Would it be possible to prefix the request url with the current root url?

For example when you translate your shop to French the root url will be /fr.
The ajax request to /cart.js fetches the products in the default language.
The products will be translated when you change the request to /fr/cart.js.

As a side note this should be mentioned in the docs as well:
https://shopify.dev/docs/themes/ajax-api/reference/cart