If purchased on delta.com, the underlying fare class can be found in the email receipt that Delta sends out in the "Fare Details" section. For example --

Fare Details: YMQ DL X/DTT DL AZO326.00QAUNA0MQ CAD326.00END

The above shows a QAUNA0MQ fare basis code which is Q fare as it starts with Q. This is a main cabin fare as identified by the second to last letter being an "M". If this fare was purchased as a C+ ticket, it would be QAUNA0CQ where the second to last letter is now a C. The underlying fare class remains 'Q', but DL will show it as a 'W' booking class. You need a Y/B/M/H/Q/K underlying fare class/main cabin fare to upgrade with miles on international. On domestic flights, L/U/T fares also qualify. X/V/E classes cannot be upgraded. The lower the fare class, the more miles it will take to upgrade.