primary_nav variable is empty on frontpage

Hello,
I'm trying to customize my theme frontpage, using the hook "page--front.tpl.php"

The hook is working, but I can't have the primary nav displayed on it.

On classic pages, the primary nav (=main-menu) is shown properly using the following code :

<?php if (!empty($primary_nav)): ?>
    <?php print render($primary_nav); ?>
<?php endif; ?>

<?php if (!empty($secondary_nav)): ?>
    <?php print render($secondary_nav); ?>
<?php endif; ?>

<?php if (!empty($page['navigation'])): ?>
    <?php print render($page['navigation']); ?>
<?php endif; ?>

On page--front.tpl.php, menu is not displayed.
$primary_nav returns "FALSE" and $main_menu is null until they are correctly filled in classic page.tpl.php

Any ideas about this problem ?
Thanks