Have you considered laying a few tarps down on the ground around the trunk, might cut down the amount of water in what sounds already saturated?

Erika,

Most likely, your tree will survive the rains. You, however not get much in the way of fruit this year. What fruit does ripen is likely to not taste too good.

The yellowing of the leaves is due to leaf rust. It is prevalent in moist air. It is not so much caused by the amount of moisture in the ground. So tarps aren't likely to help with that issue. Furthermore, if your tree is well established, the roots have spread beyond what one could effectively tarp.

Here are some related threads:

Do these fig leaves have rust on them?

Fig Rust

It rained so much..

~james