Piers Plowman - I spose you've come across the Goliards, with their bawdy pub-songs dating mainly from the 12th and perhaps 13th century? For a sample listen to some of the stuff from Naxos, for years they have been producing high quality low cost recordings of medieval and antique music.
One I'd recommend is "Carmna Burana" (not the opera by Orff, but the name given to a manuscript collection of songs and musical notation discovered at the monastery of Beuren in Germany. Orff based his rather different opera on this). There have been lots of groups 'interpreting' medieval music since the 60s, and the results are amazing to listen to.
Carmina Burana - medieval version
Another label worth looking out for is Helios, they have an excellent collection of ethereal courtly love songs from the time of the court of Eleanor of Acquaitane that'll knock your socks off -
Courtly Love Songs
These groups have researched their subject as carefully as they can and have done all possible o make the musical experience as authentic to what is presumed to be the medieval version.
There has been a lot of debate in recent years on whether or not these modern recreations of medieval music are actually authentic or not. See for example "Medievale o neomedievale?" in "Medioevo" Sept 2007, No.9 (128) 2007, p.82 -88 (pub. by DeAgostini Periodici srl, via Giovanni da Verrazano, 15 - 28100, Novara, Italy)
But this obsession with authenticity may be a more modern phenomenon since troubadors, as I understand it, didn't have 'given' versions of songs and they all interpreted them as they saw fit. Occasionally the audiences insisted on them being changed also. Maybe the idea of the 'original / authentic' version has arrived with the era of sound recordings?
Anyway, bit of thread drift there, getting back to the thread, there are some rather interesting songs available as a CD soundtrack to 'Wickerman' which though no doubt they are not 'authentic' whatever 'authentic' means here, are worth listening to anyway.