During the 14th century, a fashion for pointed toes spread across Europe. The style seems to have originated in Poland as it became known as the poulaine (from "Poland") or the cracow (from "Krakow"). Within a hundred years, the fashion would change to shoes with very wide toes. The word "poulaine" refers to the pointy toed style, but you will often hear them called "turnshoes" because of the way they were made. The shoes were sewn inside-out and then turned, instead of having the welted sole of later periods.
The funeral brass of Lady Alyne de Creke, dated 1325 - 1340, shows her pointy toes sticking out from under her cotehardie and sideless surcoat.
Our shoes are actually a modern Spanish fashion, designed to look medieval. Plus ça change...