It occurs to me that we are looking at this from the wrong direction. What is meant by 'folk', and what is meant by 'jazz', 'pop', 'rock', 'classical' or any other genre of music is essentially a question of style and structure. Within any of these labels there may be a wide range of styles - Dixieland jazz sounds very different from bebop, Mozart sounds very different from Stockhausen. However by convention styles can be grouped within particular labels, although the edges may be blurred (and individual pieces or performances may defy categorisation). They are nothing more than a convenient way of knowing which section of the record shop to head for and a convenient shorthand description. To discuss any of them in more detail requires more precision of language and a different vocabulary

What makes it so difficult for us is that within the 'folk' categorisation is a particular body of music which is defined by its origins. Fr various reasons some of us (although by no means all) place a particular value on this. However we don't have an agreed term to describe this - or rather we did, but this has been usurped to describe the category as a whole. We therefore use the same word in two different ways. This is not unusual in the English language, and usually it is perfectly obvious from the context which is meant.

To return to the original question, a new song can only become a 'folk song' if it goes through a process of acceptance and moulding by a community of people which turns it into something different from the original. However it can still be 'folk' if it meets the accepted stylistic conventions which that label implies.