First of all this ,second fig is not Longue D'Aout.
As to what it is,I would not be worried if I was you.
Because if it drops in your place it will drop in many other climates.
Why it drops:
-Even if self fertile ,drops because is not adapted to your climate,and many others.
-If is cauducous and needs pollination,again is of no use to 99 percent of gardener in the us.
-My opinion:Do not sell it,get rid of it,in dumpster,so no one will have your frustration.
Keep,the real one and ,sell as many as you can.