Hi Laurent,
We are a team who are experienced in PHP, MySql, Ajax, JQuery, JavaScript, Wordpress, Joomla, Magento, Prestashop Open Cart etc.
After going through your description ,I beleive I can do this Joomla basket for you.I have some doubts also on it.
You can check our portfolio:
I would like to discuss more with you
Regards,
Alisa