Thanks Parrot for that hint. It is not described in the manual, but it works as expected:
It is easy to brick the radio when modifiying system files!
Rooting the radio therefore is dangerous if you don't know what to do.
However there is a way to recover the radio, as long as the bootloader is still working.
Parrot's support gave me that nice hint, so I'll share it with you:
In case your car stereo is no longer booting normally, so that you can't access the "update" menu, you can reflash a firmware file with this method:
1. Turn your car stereo off.
2. Plug in an usb key containing the *.plf Update file
3. While powering the radio on, press and hold both the voice recognition button and the big parrot button.
4. The update utility will start and flash the plf-Update from your usb key.
5. After a reboot, you have a factory fresh car stereo.
All data will be deleted.