Medieval babies had a very bland diet. Of course, the youngest infants lived on breastmilk, but it was rare for a wealthy woman to nurse her own baby. Families who could afford to hire a wet nurse did so, and they believed that the wet nurse’s general health and even moral character would pass to the baby, so they tried to hire very carefully. (The tradition lasted for a long time; the infant Jane Austen lived most of her first two years at a neighboring farm, with her parents only visiting once or twice a week.)
Once weaned, the young child ate a small range of foods. Doctors believed that most food would make babies sick. The standard food was bread soaked in milk, the precursor of the Victorian nursery’s rice and bread puddings. We know little of what babies ate unless a book from the period tells us; one 13th century book permitted apples and eggs if they were handled carefully. Apples had to be peeled and were probably cooked; eggs were soft-boiled.
When these babies needed to drink something other than milk, they usually got weak ale. Juice didn’t exist in the form we know it, and water was often unsafe unless boiled. Fermenting wheat in water to make ale was the standard way to disinfect and store it. The alcohol content was low and children were accustomed to the taste from their earliest years.