I'm using FreeCAD, and I would like to duplicate a 2D sketch on another plane, but I can't seem to find an obvious way to do this.
I’m assuming you are working in the Part Design workbench. Select the sketch and click Edit->duplicate selected object. Make sure that only the sketch is copied (depending on the version, either deselect the plane or click don’t include dependent objects). This will produce a duplicate sketch in the active body (if you want the duplicate in a different body, make sure it’s active first by double-clicking it if necessary). You can then click Part Design->reorient sketch to move it to a different plane.
By the way, FreeCAD has a very active and helpful forum at https://freecadweb.org. I highly recommend asking FreeCAD questions there.