You can pinpoint a SharePoint metadata field to a specific term within a term set, so on a high level you would have Taxonomy tree and Folksonomy tree under single Term Set and point Taxonomy field to the Taxonomy tree and Folksonomy field to the Folksonomy tree.
However, if your folksonomy by definition requires users to be able to tag content without having modify permission to the actual content item, you may need to implement some custom solution that allows "tagging" content using folksonomy without actual SharePoint list item permission to edit the item.
The HashTag/enterprise keywords functionality of SharePoint 2010/2013 forces you to use the default term set that is outside any custom Term Set.