Finches usually eat seeds, but to mantain optimal health they also need other finch food. In the wild nature finches they know by instict which type of nutrition they need and try to locate a food source. They eat wild berries, sap or fresh greens.
Inhouse the finches cat be adapted to other food, but you have to pay attention to feed them correctly. The main part of finch food should be made of seeds, like in nature but you have to provide other supplements to keep them healthy. You can try to feed cooked white or brown rice, peas, green beans, strawberry, grape, mellon or corn. Finch pellets are not so suitable because they are too big and don’t look like usual food to finches.
Bird supplies offer different special nutrients for birds, you can feed them from time to time with this extra bird nutriends. This will avoid shortage of needed mineral nutriens or vitamins.