Triggering the Feed Import module
Based on @Gaydabura clues, I've created a module.
Here's the answer :

1. use hook_menu to define you own path

function toot_menu() {
  $items = array();
  $items['toot/import'] = array(
    'page callback' =&gt; 'toot_callback',
    'title' =&gt; 'Import tool',
    'access arguments' =&gt; array('access content'),
    'type' =&gt; MENU_CALLBACK
  );
  return $items;
}


2. write function using docs to parse your data

function toot_callback($key = '') {
  if ($key != 'defined_key') {
    return t('Unauthorized access');
  }
  else {
    $myFeed = feeds_source('feed_unique_id');
    while (FEEDS_BATCH_COMPLETE != $myFeed-&gt;import());
    return t('Import successfull');
  }
}