Respectfully, I have to disagree with others. It is not Fig Rust, it is- Anthroacnose (Collectotrichum). Symptoms of fig rust usually start from the edges of the leaves, not in the middle. Plus, fig rust's spots (visible fungal colonies) are much smaller and closer together. On the other hand, with Anthroacnose, the dark colored spots are spaced widely and unevenly in the middle of the leaves.
With both disease, I remove the leaves, especially with Anthroacnose, it is much serious than rust. After years of using the Copper sprays, I have came into the conclusion, it doen't work 100% of the time and sometimes it will burn the very young leaves with in 2-3 days of its application. Chlorothalonil (barnd name- Daconil), has worked best for me.
Good luck,
Navid.