OK, I started working on implementing artworkad's idea.
First thing I did was updating FOSUserBundle to 2.0.*@dev in composer.json, because I was using v1.3.1, which doesn't implement the FOSUserEvents class. This is required to subscribe to my registration event.
// composer.json
"friendsofsymfony/user-bundle": "2.0.*@dev",
Then I added a new service :
<!-- Moskito/Bundle/UserBundle/Resources/config/services.xml -->
<service id="moskito_bundle_user.user_creation" class="Moskito\Bundle\UserBundle\EventListener\UserCreationListener">
    <tag name="kernel.event_subscriber" alias="moskito_user_creation_listener" />
        <argument type="service" id="doctrine.orm.entity_manager"/>
</service>
In the XML, I told the service I needed access to Doctrine through an argument doctrine.orm.entity_manager. Then, I created the Listener :
// Moskito/Bundle/UserBundle/EventListener/UserCreationListener.php
<?php
namespace Moskito\Bundle\UserBundle\EventListener;
use FOS\UserBundle\FOSUserEvents;
use FOS\UserBundle\Event\FormEvent;
use Symfony\Component\EventDispatcher\EventSubscriberInterface;
use Doctrine\ORM\EntityManager;
/**
 * Listener responsible to change the redirection at the end of the password resetting
 */
class UserCreationListener implements EventSubscriberInterface
{
    protected $em;
    protected $user;
    public function __construct(EntityManager $em)
    {
        $this->em = $em;
    }
    /**
     * {@inheritDoc}
     */
    public static function getSubscribedEvents()
    {
        return array(
            FOSUserEvents::REGISTRATION_SUCCESS => 'onRegistrationSuccess',
        );
    }
    public function onRegistrationSuccess(FormEvent $event)
    {
        $this->user = $event->getForm()->getData();
        $group_name = 'my_default_group_name';
        $entity = $this->em->getRepository('MoskitoUserBundle:Group')->findOneByName($group_name); // You could do that by Id, too
        $this->user->addGroup($entity);
        $this->em->flush();
    }
}
And basically, that's it !
After each registration success, onRegistrationSuccess() is called, so I get the user through the FormEvent $event and add it to my default group, which I get through Doctrine.