elemind

Plugin will allow you to fetch the WP REST API call with a “lang” variable. 
It will retrieve the right content from WPML.
Tested with the latest version of:
<ul>
<li>WPML 3.2.7</li>
<li>WP REST API 2.0-beta4</li>
</ul>

WP REST API multilanguage (over WMPL)

Allows you to request a language with your WP-API and WPML site.

Quicksnail Plugins

API Press is a free WordPress JSON API integration plugin that lets you easily connect external APIs to WordPress — no coding required.
Setup and manage unlimited API connections, right from your WordPress admin. You can define the API endpoint and add query parameters, headers, body data and authentication settings.
Click Send to see the response and then use the shortcode or template tag to display the data anywhere on your site.
If you have ever used Postman for API integrations, API Press will be very familiar. It is a low-code / no-code API connector plugin for WordPress to connect to JSON API.
Simple and flexible API connector for WordPress.
<h3>JSON API Connector Features</h3>
<ul>
<li>Unlimited integrations</li>
<li>Works with all REST APIs</li>
<li>GET, POST, PUT, PATCH & DELETE HTTP methods</li>
<li>Query parameters, headers and body data</li>
<li>Cache APIs</li>
<li>Logging of all requests </li>
<li>Send raw JSON, form-data and x-www-form-urlencoded body types </li>
<li>Preview responses directly in the admin</li>
<li>Use shortcode or template tag to output API data anywhere on your site</li>
<li>Authentication options: API Key, Bearer token, Basic Auth, no auth (OAuth 2.0 in <a href="https://api-press.com/downloads/pro-plugin/" rel="nofollow ugc">PRO</a>) </li>
<li>No code</li>
</ul>
<h3>API Press PRO Features</h3>
<ul>
<li>Templates – Output responses with pre-built templates – Gallery, Table, Carousel etc.</li>
<li>Triggers – call API on WordPress actions (e.g., when a user registers or a form is submitted) </li>
<li>Variables – dynamically send user data, post data or site data to your API </li>
<li>OAuth 2.0 Authorization (oauth2) </li>
<li>Auto HTML formatting for displaying API responses </li>
<li>Email alerts on failed responses</li>
<li>One-click cloning</li>
<li>Preview API request before sending</li>
</ul>
View the <a href="https://api-press.com/downloads/pro-plugin/" rel="nofollow ugc">API Press PRO</a> plugin.
API Press is an easy to use WordPress API integration plugin that is ideal for developers, site builders and businesses that need a flexible, no-code way to connect APIs inside WordPress.
<h3>WordPress API Integration Plugin</h3>
Using API Press is simple: To connect your API to your WordPress site, simply install this plugin and then visit API Press in your admin to add a new API. Fill in the details of your API including URL and any headers, query strings, body parameters or authentication and click Send.

API Press – API Connector for JSON APIs

Postman style WordPress API plugin. API connector to send API data, preview responses & display data with shortcode or template tag.

WP REST API multilanguage (over WMPL) vs API Press – API Connector for JSON APIs