Here's the solution : use ClientLogin authentication. That allow us to specify our YT credentials through this line :
$httpClient = Zend_Gdata_ClientLogin::getHttpClient($youtubeEmail, $youtubePassword, 'youtube');
NB : The third parameter is the "id" of the service we want to connect to
I know ClientLogin is deprecated but this solution work. If there is any solution more secure and clean, let me know :)
Have a nice day