I’m not a Mac user so I’m not sure exactly what you moved. If it was the Fritzing application folder, you should be able to delete it and reinstall it without problem (the user files are in two other directories.) If the user directories (which sounds likely) are what you moved they should be in:
/Users/username/Documents/Fritzing/parts
and
~/.config/Fritzing
(where username will be the account name you are moving to.)
on a Mac. So copying them there with Fritzing not running should fix up your installation . Fritzing will have created new copies when it ran and found them not present, so you likely need to rename them for safety before copying your original files in their place. Once you are stable, you can delete both the unused copies of the user directories to save disk space.
Peter