Nobody writes a 'folk song' - they never have - they become such via a process - very much a case of 'don't call us, we'll call you'            
nevertheless the song is still written by someone, it succeeds in becoming a folk song if it is taken up by people who assume its tradtional, examples that spring to mind are fiddlers green, shoals of herring,bring us a barrel.
all songs have been composed by someone, some like 3 score and ten get altered and improved by someone other than the original author.
it is possible that someone could set out with the intention of writing a folk song, by using certain modes and certain speech rythyms, whether they succeed is actually up to the people, but there is no reason why it is not possible to write one intentionally,
isnt that what broad sheet writers did, set out to write songs about specific incidents and then sell them, that was the intention of broadshet writers to deliberately write songs that would sell, broadshett songs are often considered folk songs, check mate jim