I have made several batches of fig wine but fig mead is my favorite. Another used a blend of fresh and dried figs, 5-6# fresh/1# dried per gallon. Dates and bananas make great add-ins too. Unfortunately this is one wine I always add a bit of this, more of that to, no recipe kept. I like Montrachet and Premier Cuvee and Cotes de Blanc for this one, and a year minimum bulk aging.
Fresh figs if frozen/thawed will yield a great amount of juice too. Think about adding some spices, like vanilla, star anise, cardamom (chai blend would be great). Since figs are quite sweet tread lightly on sugar/honey addition initially. You get a better idea if you wait 24hr after enzymes and another 24hr after k-meta, then check SG and adjust it.
Do you know the cultivar of this fig tree, or the skin/pulp color? I have 50+ different cultivars of fig trees growing in containers right now, quite enchanted with them. Weird, I know.