It's difficult to say what could cause brown edges on houseplant leaves. Fiddle leaf figs can be a bit fussy as houseplants. They tend to be sensitive to being moved and having temperature changes. It could be from over watering or under watering too. Does the container have drainage? Is there a saucer under the container where water is sitting? Has the plant been recently repotted, or perhaps it needs to be? 

If the soil is too wet, wait for it to dry out and monitor it between watering. It should be dry in the first 2 inches or so before needing to water again. It may have root rot if it has been consistently too wet for too long, but you could wait to see if it gets new growth on the upper stem first. Since it is a tropical plant in its native habitat, it prefers humid air and often inside our winter homes it is too dry. If you are misting the leaves, we would recommend that you stop as this can cause leaf disease issues. If you need to dust them, a slightly damp soft cloth can work.

University of California has an article from their Master Gardener Newsletter that is helpful: https://ucanr.edu/blogs/blogcore/postdetail.cfm?postnum=46029

You will have to wait and see if the conditions worsen. 

Let us know if you have further questions. 

Emily