A payment may be successfully processed even if you receive a notification error email from Payplug. Payment processing and notification delivery are two separate mechanisms: the first collects the funds, while the second updates your website on the status of the transaction. One can succeed even if the other fails.
Your payment is not affected. The customer has been charged, the funds are collected in your Payplug account, and you can find the transaction under the Payments menu in your portal.
What failed was the transmission of this data to your store. Depending on the scenario, your order may remain pending, fail to be created, or fail to trigger automated emails.
To identify and resolve the issue, please refer to What to do in case of a notification error?
If you have not received an error notification and the order still does not update, see The payment went through, but the order is not updating on my CMS.