You're asking the wrong question. Blues didn't come about because the guitar existed; the guitar had nothing to do with it.

Blues came from the influence of the African culture and musical tradition influencing the music of the US. In the ante-bellum south, the slaves would sing spirituals, which come from the work chants, which has its origins in African call and response styles of singing, and syncopated rhythms and drumming. If you listen to the original slave work songs, you can hear the origin of the blues. But it was all sung, and occasionally had percussion, but instruments came much, much later.

The spirituals became minstrel shows, which became early blues, which became jazz and rock, which are both offshoots of blues. The guitar came into play much later.

As for folk music, there's a ton of it, but it's played on the folk instruments of the region. It's also rarely written down. The guitar of the 1300s was not a folk instrument - it's a classical instrument. Folk instruments of Europe would be small flutes, pipes (bagpipes are a good example), and smaller instruments that regular people could easily make and play.