It's really just a matter of personal preference; there's no "right" way to deal with it. If it were my tree, I'd almost certainly just prune off the broken part. Young, healthy fig trees are very resilient.
I used to think I wanted all of my figs to be single trunked for at least a foot or so out of the ground, but now, as I see all of the healthy-looking branches coming up from just above or below the soil line, I'm leaning toward letting at least some of them remain bushes. After all, there will likely be more fruit, closer to the ground, easier to pick, and more foliage to shade the "trunk." But, if I change my mind, I can always prune off the lower branches--at least while the tree is young--and the pruning cuts should heal over. Some of the new suckers one one or two figs are so much more vigorous than the original leader that I'm considering pruning off the "original" growth and turning the sucker into the leader. Who knows? I'll just play it by ear.
So, even if you remove the broken part and it shoots out several new branches, you still have plenty of options about what shape you prefer in the long run.