Default/fallback language breaks pagination

I tried a completely different approach. That’s a plugin (and no more a theme hack).

<?php
/*
Plugin name: Fallback to Polylang default language
*/

if (defined(POLYLANG_VERSION)) {
	add_action ('pre_get_posts', 'pll_pre_get_posts');
	add_action ('wp', 'pll_wp');
}

function pll_pre_get_posts($query) {
	global $polylang;

	if (!$query->is_main_query())
		return;

	unset($query->query_vars['lang']);
	$polylang->choose_lang->set_lang_query_var($query, $polylang->model->get_language($polylang->options['default_lang']));
}

function pll_wp() {
	global $wp_query;

	if (!$wp_query->is_main_query())
		return;

	foreach (wp_list_pluck($wp_query->posts, 'ID') as $id) {
		$tr_ids[$id] = pll_get_post($id);
	}

	foreach ($posts = get_posts(array('include' => $tr_ids)) as $key => $p) {
		$tr_posts[$p->ID] = &$posts[$key];
	}

	foreach($wp_query->posts as $key => $p) {
		if (!empty($tr_ids[$p->ID])) {
			$wp_query->posts[$key] = &$tr_posts[$tr_ids[$p->ID]];
		}
	}
}