Q.Will Rootstock Sprouts produce fruit?
While removing some dead trees from the back of our land, the workers accidentally broke our peach tree. It was about 4 inches around. We tried to graft it back together, but the tree eventually fell over. There are several shoots coming out of the base of the tree, perhaps 1 inch off the ground. I was told that shoots do not produce fruit. Is this true?

They peach tree was likely a grafted tree and the root stock is from another tree of some kind.
The root growth likely would not be a Peach tree variety. It is best to dig up and remove and start a new tree.
I'm sorry your tree was lost.