If it was not you, can you not start by identifying which shop was involved, on precisely what date and time. I would also ask for details of the complainant - how the crime was reported, the name of the officer involved, and details of where the arrest took place.
This should start to give you some clues - was it a place you normally shop, if so do the staff know you there and again if so, ask if they remember the incident and why were you not banned from the shop "if they caught you shoplifting".
If it was somebody who gave your name and address, how wide of the mark was the postcode and date of birth. Particularly with the date of birth, if they gave say a date in 1990 which makes you a teenager and you are in your forties, and was accepted, then clearly it can be shown to be a fraud. On the other hand if it is close...... ? Is the postcode nearby ?
I think you need to get a lot more detail to start picking holes in it!