Typically, grafting is done in spring, for my location it is March to April ideally yet I have had some success later in the year. The main importance with grafting is matching up the vascular cambium layer, followed by properly securing the Scionwood and sealing the cutting to prevent it from dying out. Also, the tree should be 2 or 3 weeks ahead of the scionwood. Meaning the scionwood is still dormant while the tree is starting to bud out.
Again, I have yet to graft a fig, I only have experience with stone fruits, apples and pears.
Scott