If I attach a Basic Fighting Energy to Eevee, can I use its "Energy Evolution" Ability even though it's known that there's no Fighting type Pokemon that evolves from Eevee?
No, since it's known that there is no Fighting type Pokemon that evolves from Eevee, the Ability cannot be used.
Source: Furious Fists FAQ (2014-08-28), TPCi Rules Team (2014-08-28), TPCi Rules Team (2023-06-22)

Relevant cards

Note: All applicable cards may not be listed below.
XY3_80