Mailchimp offers a Pop-up to activate on your site to promote subscription to your newsletter. All the configuration is done directly with Mailchimp, but if Mailchimp proposes to integrate a specific code to your shop, it is because there is a problem of association with your shop, so you must dissociate it and then resume the complete synchronization of your product catalog with Mailchimp.
Prestashop integrates a default registration form on your pages. As with everything else, synchronization is done in real time and automatically.
If you already had email addresses registered in this module, you will have to make a manual addition to Mailchilmp because, basically, this form is not able to register the client's language, so the PrestaMailchimp module is not able to do this initial synchronization.