Chilmark, Marthas Vineyard, MA
One of the nice things about Christians is that they really, really want you to know about the Bible. In service of that goal, they have created bajillions of websites that cover the minutia Bible in exhaustive detail. The Christian website I use for names is good for my purposes because it has lots of useful glossaries and tends to quote the King James Version (KJV), which would have been familiar to the residents of colonial New England (they also used the Geneva Bible, but that one isn't really so popular on the internet and it's similar to the KJV). Wikipedia also has an impressive list of Biblical names, but the spellings are not always taken from the KJV, so they seem less likely to show up in colonial New England.
The detail-oriented people at christiananswers.net assure me that there are only 3 names beginning with F in the whole Bible: Felix, Festus, and Fortunatus. The first two were certainly Romans and the third probably was — in any event, they are all in the New Testament. Colonial New Englanders liked to use Old Testament names — you won't find many Pauls or Lukes in this crowd — and none of these three names seemed particularly outlandish to me. I picked Fortunatus because he seems to be a relatively obscure character (1 Cor. 16:17).
Obscure Bible Names Alphabet