connect CRM to Prestashop to assist our email customer support

I run an e-shop in Prestashop and am looking around for a CRM that will help my business.

I’m specifically looking for a feature where I can integrate the CRM with Prestashop and make our email customer support easier to handle than what we’re currently using.

Our current flow:

1. Customer places order, an order email goes out to him and to us.
   Since we get the order email we always have a history of each order in our support mailbox (gmail).

2. A customer writes to our support team asking for this and that, where is my order?, can I return? how do I return? does product A have feature B? etc etc.

Now our support worker (one one at the moment) searches in the mailbox for the customer’s order to be able to find it and know what the customer is talking about. Sometimes she even has to do an extra search directly in Prestashop for the specific order. Very archaic.

I know that this is not a very efficient way to work and there must be an easier way.

What I’m looking for is this:

Whenever a customer sends an email to our support team I want all the orders for that customer and all the email threads and so on to already show nicely in a threaded view.

Our support worker should never have to make extra searches inside the mailbox or in Prestashop. Everything should just be there from the beginning! All customer orders, all email back and forth and so on.

We will add more support staff and so the support mailbox will be shared among all. The system must be able to handle that a support worker can “pick up” an email to work with so everybody else of our support staff will know to take another email to work on.

I have started playing around with Hubspot but am not sure whether it does what I need. Either that or I don’t know what to look for in there.

All this really seems like basic features. Can someone help me by pointing me in the right direction?

Thank you all!