While completing the LTW level 30 class quest, "Design Imposters", I was asked to create a "Fen-Yll Birkin Bag". The description of the item when preparing for synthesis is as follows:

"A pair of designer shoes, easily discernable as a product of Atelier Fen-Yll. The demand for such footwear is enough to drive lesser men to crime..."

However, if Wikipedia is to be believed, a Birkin Bag is a very high-end leather handbag (created for and named after actress Jane Birkin; perhaps there's someone with a similar name in Eorzea.) It's certainly something that brigands might eye greedily, but I can't see it as shoes. (The NPCs encountered in the course of the quest also refer to it as a bag, for what it's worth.)