That sounds a little strange. A .fz file is an uncompressed sketch (document). A .fzp file is a part definition file. A .fzp file by itself is not a full part. It should have (up to) 4 .svg files with it. Usually the .fzp and .svg files are packaged togehter as a .fzpz file. A .fz is usually packaged as a .fzz, which can be opened directly, and contains any custom (non-core) parts it needs. Which includes the .fzp and .svg files.
Did that “library set” come as zip file? Maybe a .fzz file? If you provide a link to where you got the “library set” from, we can have a look to see what it is really doing.
Opening a .fzpz will add the part to the MINE bin, and put the files where they belong. Probably (for windows)
c:\Users\username\My Documents\Fritzing\user
c:\Users\username\My Documents\Fritzing\user\svg\user\breadboard
c:\Users\username\My Documents\Fritzing\user\svg\user\icon
c:\Users\username\My Documents\Fritzing\user\svg\user\pcb
c:\Users\username\My Documents\Fritzing\user\svg\user\schematic