wordpress: change language for theme only

functions.php

<?php

// load default translated strings based on locale
load_default_textdomain();

//  theme translated strings, modify as you need
load_theme_textdomain( 'zatheme', get_template_directory() . '/languages' );

plugin.php

<?php
/**
 * Plugin Name: plugin
 * Description: plugin custom
 * Version: 1.0.0
 */

// prevent direct access
defined('ABSPATH') or die();

add_filter('locale', 'zatheme_locale');
function zatheme_locale($locale) {
    if ( !is_admin() ) {
        // modify as you need
        $locale = 'en_US';
    }

    return $locale;
}