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.

arminmeth

While WordPress is slowly but surely becoming a complete application framework and JSON REST API is huge step in this direction, there is a large number of WordPress users that do not need advanced features like those offered by WordPress JSON REST API. This plugin helps them to turn those advanced features off and not worry about it.
While other similar plugins disable JSON REST API functionality only for anonymous users, Kill JSON REST API completely disables the framework for all users and removes links and tags from head element.

Kill JSON REST API

Completely disables JSON REST API for both registered and anonymous users in WordPress 4.7.* and removes API links and tags.

WP REST API multilanguage (over WMPL) vs Kill JSON REST API