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.

Ryuhei Yokokawa

Plugin will allow you to fetch the WP-API (WP-JSON-API) call with a “lang” variable. It will retrieve the right content from WPML/WP.
This only works with WPML and WP-API installed. I tested only with the latest version as of now: 
* WPML 3.1.9.6 
* WP REST API 1.2.1

WP REST API multilanguage (over WMPL) vs WPML to WP API