"Failed to connect to worker process" is an error message from Calibre failing to correctly spawn a background job to run the download.
I don't think there's anything specific to FanFicFare that could be causing it. I suspect you'd see the same thing trying to run Convert or other background jobs.
I would try:
- Check to make sure your hard drive isn't full.
- Reboot your computer
- Reinstall FanFicFare
- Reinstall Calibre
- Run Calibre in debug mode (under the Preferences dropdown) to see if it gives more useful information.