The only mention of the name Fowey that I can find comes from I D Spreadbury's, Fowey: a brief history. He says that Fowey has always been pronounced the same way, but has been spelt in a variety of ways, Fawi, Fowy, Vauwy, Foy, Foye, for example. The river was named Fawi, long before it was applied to the town. Fau in Cornish means beeches and there are beeches lining the river.(Both pronounced Fowey) The spelling of place names was not standardised until about 1900's so most were spelt phonetically.Although this does not answer your specific question, I hope that it helps. I will keep looking and if I find anything else I will let you know. Lesley Woodhouse
The above seems to confirm independently that Foy, Foye and Fay are derived from the Latin "Fagus" or Cornwallian "Fau" meaning Beech.