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

elemind

WP REST API multilanguage (over WMPL)

Pete Nelson

REST API Toolbox

Allows tweaking of several REST API settings

Ali Qureshi

JSON API User

Extends the JSON API Plugin to allow RESTful user registration, authentication & many other User Meta, BP functions. A Pro version is also available.

JSON API Auth

Extends the JSON API Plugin for RESTful user authentication

JasmanXcrew

REST API Helper

This plugin help REST API for display featured media source, author, categories, and custom fields.

arminmeth

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.

JSON API Cincopa

Extends the JSON API Plugin to allow RESTful Cincopa Easy Albums Listing for any user

digitalissimo

Get Json Api

Retrieve the results of the API of a site that uses the plugin JSON API

youzu_bigapp

WP-BigApp

This plugin provide json api and the web master could create app for phone.

aiyaz Khorajia

JSON API Delete User

Delete User with meta details add-ons for JSON API

Rajat

Restrict Json Rest Api

Plugin to restrict json rest api, which you want to restrict to use from outside

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

Alternatives to WPML to WP API

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