There is much less secular music surviving in written sources, but there is some. There are also cases where the lines between the two blur somewhat, like the Cantigas de Santa Maria, and the Llibre Vermell de Montserrat, or "Sumer is icumen in" redone as "Perspice christicola." You will have to do some reconstruction and a lot of interpretation, and have the research to support THAT, as well. The good thing is that a lot of the folks who do early music well also take an interest in educating people about it, and are more than willing to talk to folks about the research they've done and why they choose to perform a piece the way they do. My favorite is Hesperus but there are others, too... good luck!