New shoots will sprout from below the cut, just be patient. Remove the fruit from your cut branches. I recommend cutting the branch every two nodes, leaving a leaf or two at most per cutting. Then take the cuttings, wrap them in a damp newspaper, put that in a plastic bag and keep somewhere warm. If things go well and mold does not strike you should be able to get most of these cuttings to start roots.

i've never tried to graft so somebody else can answer to that.

Sorry this happened, but as long as you have roots, the tree will come back. You won't get fruit this year, but probably next year. I'm assuming this was a one trunk tree. You may end up with a multi trunk tree, which is just fine. You can keep it a manageable size and more trunks mean more fruit, OR you can choose one of the new sprouts and train it to be a main trunk.

You say the fruit was small, not fully ripe and not edible. I'm wondering if you have a seedling fig that really isn't worth saving. Some of those need pollination from the fig wasp, and if that's what you have, the fruit may never be good. Why didn't the fruit get ripe? I have figs in the shade, and they ripen fruit. It just seems odd to me. Most fig trees that are one or two years old will ripen fruit.

There is no way to tell what you have until the tree grows back. Good luck to you!

Depending on where you are, the figs may not have gotten enough warmth and sun to ripen the fruit. I'd give it a couple of years. If it doesn't produce, you can always try to graft a different variety onto the existing root stock. Your tree should have a wonderful set of roots to support the graft.

If there are breba figs (on last year's growth) cut some open and look for male flowers around the eye. If it was crowded and still a young tree it may not have been planted at all but a male seedling that will never be edible.