Use code as below :
<?php
$myotherdatabase = new wpdb("username","password","databasename","localhost");
$motscles = "abri";
$query = "SELECT `post_id` FROM `wp_postmeta` WHERE `meta_key` = 'nom' AND MATCH (`meta_value`) AGAINST ('" . $motscles . "' IN BOOLEAN MODE)";
$result = $myotherdatabase -> get_results($query, ARRAY_A);
foreach ($result as $post) {
$pids .= $post->post_id . ",";// ARRAY_A
}
echo $pids;
?>