If I have Florges with "Calming Aroma" in play my attacks cost one Fairy Energy less. So I think I can use Zygarde's "Core Enforcer" attack without a Fairy energy attached, but what about the part of the attack that says to discard one Dark and one Fairy energy from this Pokemon?
You do as much of the attack text as you can, which in your situation means simply discarding one Dark energy.
Source: TPCi Rules Team (2017-09-21)

Relevant cards

Note: All applicable cards may not be listed below.
SM3_100
XY8_103