Lots of people have had excellent luck in pinching off the tip of new growth. This promotes branching as well as fig production. When you fig comes out of dormancy and starts new growth, wait until you have 3-5 new nodes and then pinch off the tip of the branch. You should see some branching after that. You may get some suckers too, they're all good (but maybe not too many.)

Max figs = max branching = open vase/bush. Do a google image search for "fig pruning" to see what shape you can deal with i.e. protect in winter. Most people grown figs for figs and prune well before it naturally branches.