pelerine

A kind of short cape or covering for the shoulders, associated especially with medieval pilgrims (of any gender).

[…] Around his shoulders, he wore a thick gray pelerine. This was the custom of the knights of the Kingdom of the Spears, the land of the beaches and the chalk cliffs with great castles[…]

Beneath the pale light crouched an ancient white-haited man, wrapped against the rain in a threadbare maroon pelerine. “Alms, sire,” he croaked, his eyes wide and fearful, his face lean and hungry. He was so thin […]

A woman's tippet or cape with long ends coming down in front.

Pilgrims, male or female, wore gowns […] A hood was usually added, but even if that were omitted, the pilgrim wore a shoulder-cape, a custom so universal that this type of cape came to be called a "pelerine," a name still used in the nineteenth century to describe the short capes fashionable in women's dress.