I would not use a DXF-file for transfering the geometry from Adobe to FreeCAD. The DXF-capabilties of FreeCAD are limited due to the proprietary file format. You may try to get a PDF from Adobe Illustrator and import it in Inkscape. Then save the geometry as SVG in Inkscape and import this in FreeCAD. The chances are better, that you get a sufficient result.
SVG was the answer.
I exported it from Illustrator to SVG and then imported it to FreeCAD.
It worked strait away.