It's interesting.
In this case, 前 have two meanings "opposite side" and "in front of"
Therefor,その時、太郎は、店の前の前にみかんが一つ置いてあるのを見た。
⇒Tarou saw a orange which is being put in front of shop on opposite side.
But it's also possible this meaning.
⇒Tarou saw a orange which is being put in front of forward of shop.
Of course this is quite weird.
I hope this answer will help you.