The only tool available to edit the geometry of map frames is a simplified version of the Edit Vertices tool, and once a segment is converted to bezier curves, the user can't move the handles of a vertex between two curves independently - they are stuck with whatever angle the lines created at the time of creation.
If you grab one blue handle and move it, the other one also rotates/lengthens. Please allow these to be individually modifiable as elsewhere in the application so that users can more easily reshape their map frames.