I don't know what kind of fig tree it is, but is sure makes a big crop of tasty fruit. Boy #1 calls them 'Sugar Figs'. They don't have a really strong flavor, but they are very very sweet. The skins is kind of purple and light brown, with amber-strawberry colored flesh. I think it is most likely a Celeste, or Celeste-type fig, but I would need a fig expert to tell me for sure.
We've also been picking more of the LSU Gold figs. These are huge, fat yellow figs with yellow flesh, and a slightly thicker skin. They can taste a little watery or bland if eaten right after the tree has been watered, but when picked at peak ripeness they are very delicious, sweet with a very unique flavor. The birds seem to be ignoring the LSU Gold tree in favor of the two large purple figs planted in adjacent yards. Boy #1 prefers the 'Sugar Figs' too, but I like the LSU Gold flavor better.
Our young Celeste, LSU Purple, and South Carolina Lemon Fig trees dropped their fruit, but the Petite Negra has held onto around 15 figs. I've been babying the tree, and trying to make sure it gets plenty of water. Hopefully we'll get to taste these in the next few weeks.