Hi Evenie,
My name is Mie and I’m a tour guide. I think you might be interested in a woodblock-printed paper studio called Karacho established in 1624.The present owner is the 12th generation.
http://www.designboom.com/history/karachokarakami.html
Also, there is a paper shop called Kamiji-Kakimoto on the Teramachi street.Although it’s not a paper factory, still you’ll be able to find a wide viriety of hand-made paper with beautiful designs.
I hope this would help you enjoy your stay in Kyoto.
Thank you.