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.

Pete Nelson

Allows tweaking of several REST API settings
<ul>
<li>Disable the REST API</li>
<li>Remove WordPress core endpoints</li>
<li>Require authentication for core endpoints</li>
<li>Force SSL</li>
<li>WP-CLI commands: wp rest-api-toolbox</li>
</ul>
Find us on GitHub at https://github.com/petenelson/wp-rest-api-toolbox
(Creative commons toolbox image provided by James Tworow https://www.flickr.com/photos/sherlock77/)

REST API Toolbox

Allows tweaking of several REST API settings

WP REST API multilanguage (over WMPL) vs REST API Toolbox