Schema dot org and alternate languages - schema.org

Question

I have schema dot org markup on my website. But I also have an alternate language; each of my pages has a French version in a different page with proper hreflang tags.
Google's instructions don't really mention different languages, neither does schema dot org. For example, I have an "Organization" schema set up on the homepage. Do I need to translate it on the French homepage or leave it in English, and if so, do I change the URL to point to the French homepage as well? Wouldn't this cause Google to think there are two different organizations? Same question would apply to schemas like "Product".

Answer 1

hreflang not directly related to schema.org (That's why you didn't find any references on google/schema.org).
Schema.org is a set of extensible schemas that enables webmasters to
embed structured data on their web pages for use by search engines and
other applications. https://schema.org/
VS
Hreflang specifies the language and optional geographic restrictions
for a document. Hreflang - Google Support. The hreflang attribute on each page should include a reference to itself as well as to all the pages that serve as alternates for it https://moz.com/learn/seo/hreflang-tag.
Two pages example
**microdata (Same idea for JSON-LD). And the same idea to any schema.
Your English version
/en/about
<div itemscope itemtype="http://schema.org/LocalBusiness">
<h1><span itemprop="name">Hello World</span></h1>
<p itemprop="description">A superb collection of fine gifts and clothing
</div>
hreflang:
<link rel="alternate" href="http://example.com/en/about" hreflang="en" />
<link rel="alternate" href="http://example.com/fr/about" hreflang="fr-fr" />
Your French version
/fr/about
<div itemscope itemtype="http://schema.org/LocalBusiness">
<h1><span itemprop="name">Bonjour le monde</span></h1>
<p itemprop="description">Une superbe collection de beaux cadeaux et vêtements
</div>
hreflang:
<link rel="alternate" href="http://example.com/en/about" hreflang="en" />
<link rel="alternate" href="http://example.com/fr/about" hreflang="fr-fr" />
itemprop="name" above give extra semantic data about your LocalBusiness - each page use another language (Specify by Hreflang).
One of google guideline is:
Don't mark up content that is not visible to readers of the page. For
example, if the JSON-LD markup describes a performer, the HTML body
should describe that same performer. https://developers.google.com/search/docs/guides/sd-policies
Not official google answer about this topic - but its better to translate the JSON-LD data as well. By Wordpress or other CMS, it should be easy to pull the data.
Anyway, JSON-LD not related to site indexing (like hreflang -or- canonical). There is no need to change a URL because of a schema. You find reports (status/errors/rich results) about your schema under google search console - docs her.
Live example (From nike site):
English schema (rich card preview):
Data Testing tool
French schema (rich card preview):
Data testing tool

Answer 2

Follow the structured data guidelines of Google requires:
Relevance
Your structured data should be a true representation of the
page content.
as well as further
Location
Put the structured data on the page that it describes, unless
specified otherwise by the documentation. If you have duplicate pages
for the same content, we recommend placing the same structured data on
all page duplicates, not just on the canonical page.
Thus, if the information on your home page has a separate web page with duplicate content in French, then using structured data, you MUST set the content for data in French.
This is completely justified in terms of semantics. Google uses structured data to search for entities with API Google Knowledge Graph, for rich search results, for voice search, for machine learning. It is obvious that users using French in a web search is willing and will receive search results in French.