Yup, sketches can be exported directly as DXF in the free version.
I was trying to export complex faces made up of multiple sketches, with features applied to the bodies that didn’t appear on the individual sketches.
I did find a work-around (thanks @azab2c) by selecting the face I wanted to export, and using the “project” feature to create a sketch based on that face. Then I used the Export DXF option in that sketch menu.