Do we need a CAL for our external users if they are accessing Exchange Server 2016 Enterprise functionalities?

Yes, as soon as an external user is accessing Exchange Server Enterprise functionalities, your are required to have a CAL. This access of Exchange Server Standard functionalities are is covered by the server license.

Source: Official Microsoft Exchange Server licensing FAQ, retrieved March 2017 (https://products.office.com/en-us/exchange/microsoft-exchange-licensing-faq-email-for-business)