Deer have been known to eat peaches and actually do so much earlier than we do before they are even fully ripe. Deer tend to eat a little bit of everything, except of course meat.
Fruits like peaches and apples are certainly on the menu for these animals and they tend to eat them quite often. It is not uncommon to see a deer eating peaches that are already still on the tree or have fallen to the ground.
Those who grow peach trees in rural areas near forests and woods know that sometimes unexpected visitors such as deer come over for a bite to eat.