I searched the internet for Coach serial number G1357-F15064 and the search result showed an allegedly real version with that same serial number. Unknown if they use the same serial number over and over, and I have no knowledge of them.

https://poshmark.com/listing/Large-Watermelon-Crossbody-598f28a298182985fb0c6a7f

A highly respected expert on FIXYA, Andrew Taylor, gave a number of ways to determine.

http://www.fixya.com/support/t26074170-serial_number_h0868_12947_real