Function that adds a filter to the wp_get_navmenu_items function to filter for a specific polylang language slug.

polylang_nav_menu.php

<?php
/**
 * Displays a navigation menu based on arguments including the passed in polylang language slug.
 *
 *
 * @param array $args {
 *
 *     @type string             $language             Polylang language slug to be used. Defaults to the return of pll_current_language()
 *     @type int|string|WP_Term $menu                 Desired menu. Accepts a menu ID, slug, name, or object.
 *                                                    Default empty.
 *     @type string             $menu_class           CSS class to use for the ul element which forms the menu.
 *                                                    Default 'menu'.
 *     @type string             $menu_id              The ID that is applied to the ul element which forms the menu.
 *                                                    Default is the menu slug, incremented.
 *     @type string             $container            Whether to wrap the ul, and what to wrap it with.
 *                                                    Default 'div'.
 *     @type string             $container_class      Class that is applied to the container.
 *                                                    Default 'menu-{menu slug}-container'.
 *     @type string             $container_id         The ID that is applied to the container. Default empty.
 *     @type string             $container_aria_label The aria-label attribute that is applied to the container
 *                                                    when it's a nav element. Default empty.
 *     @type callable|false     $fallback_cb          If the menu doesn't exist, a callback function will fire.
 *                                                    Default is 'wp_page_menu'. Set to false for no fallback.
 *     @type string             $before               Text before the link markup. Default empty.
 *     @type string             $after                Text after the link markup. Default empty.
 *     @type string             $link_before          Text before the link text. Default empty.
 *     @type string             $link_after           Text after the link text. Default empty.
 *     @type bool               $echo                 Whether to echo the menu or return it. Default true.
 *     @type int                $depth                How many levels of the hierarchy are to be included.
 *                                                    0 means all. Default 0.
 *                                                    Default 0.
 *     @type object             $walker               Instance of a custom walker class. Default empty.
 *     @type string             $theme_location       Theme location to be used. Must be registered with
 *                                                    register_nav_menu() in order to be selectable by the user.
 *     @type string             $items_wrap           How the list items should be wrapped. Uses printf() format with
 *                                                    numbered placeholders. Default is a ul with an id and class.
 *     @type string             $item_spacing         Whether to preserve whitespace within the menu's HTML.
 *                                                    Accepts 'preserve' or 'discard'. Default 'preserve'.
 * }
 * @return void|string|false Void if 'echo' argument is true, menu output if 'echo' is false.
 *                           False if there are no items or no menu was found.
 */
function polylang_nav_menu($args = array()) {
    if (!function_exists("pll_current_language")) {
        return wp_nav_menu($args);
    }

    $args = array_merge(array(
        "language" => pll_current_language()
    ), $args);

    global $polylang_navmenu_args;
    $polylang_navmenu_args = $args;

    if (!function_exists("only_return_items_in_language")) {
        function only_return_items_in_language($items, $menu, $args) {
            return array_filter($items, function($item) {
                global $polylang_navmenu_args;
                $lang = $polylang_navmenu_args["language"];
                $item_lang = pll_get_post_language($item->object_id);
                return $item_lang == $lang;
            });
        }
    }

    add_filter( 'wp_get_nav_menu_items', "only_return_items_in_language", 10, 3 );
    $wp_nav_menu = wp_nav_menu($args);
    remove_filter( 'wp_get_nav_menu_items', "only_return_items_in_language", 10, 3 );
    return $wp_nav_menu;
}