Fang and Vanille are in a lesbian relationships.
The majority of the evidence comes from their interaction throughout the trilogy itself. Fang and Vanille are close. At one point, Fang and Vanille were probably lovers. But this is because:
Fang was originally written as a male character. Early in development, Lightning was meant to be a flirtatious character with more sex appeal but these traits were transferred to Fang to make Lightning a more serious character. Character designer Tetsuya Nomura has stated that when compared to the other characters personality-wise, Fang is stronger than Lightning and more stubborn than Snow.
Their relationship was also to have a mythological connection.
The characters of Fang and Vanille are based on the Ragnarok myth of Líf (“life”) and Lífþrasir (“eager for life”)—the only humans who will survive Ragnarok. They sleep through the destruction of the earth and upon awakening will find the earth verdant again. Líf and Lífþrasir will become the progenitors of a new race of humans, and their descendants will inhabit the world. This is congruent with the idea that Fang was originally envisioned as a male character.
Perhaps Fang’s original conception as a man simply carried over to her finished character design. But this means also a potential relationship between them carried over as well.
Fang and Vanille as lesbians are the stuff of fan fiction is made of.
Well, except for the fan fiction. And art.