[technothrasher]

It also makes more sense when you realize that 1) pomme in older French meant fruit generally, not apples specifically, and 2) sweet potatoes were introduced to Europe well before white potatoes were. So "earth fruit" seems fitting.

[roysting]

Technically apple is also just the general term for fruit from its root in Proto-Indo European, ab(e)l.

[wiether]

Do you have more detail about your second point?

Since they both come from America, sources I can find place them in Europe during the XVIth century.