No it should work.
Add some debug code:
<?php
if (!session_id()) session_start();
if(!isset($_SESSION["choix"])) {
die("Session set to: " . $_POST["choix"]);
$_SESSION["choix"] = "".((isset($_POST["choix"]))?$_POST["choix"]:"") ."";
}
?>
Is your form method="post"... do you have this page specified as the form action?