eAssistance Pro is an suitable option that offers live chat plugin for such a prominet using CMS, you can integrate live chat module on Prestashop created website https://www.eassista.../prestashop.php
Prestashop is such a free open source that allow to create a customizable own online store. For the chat interface, you can integrate eAssistance Pro live chat palugin for Prestashop, that enable you to add a live chat option on your Prestashop store. It's fully customizable and compatible chat module.