Downloaded and extracted to /home/pi/FreeFileSync,
.desktop reads
[Desktop Entry] Type=Application Name=FreeFileSync GenericName=Folder Comparison and Synchronization GenericName[de_DE]=Ordnervergleich und Synchronisation Exec=/home/pi/FreeFileSync/Bin/FreeFileSync_i686 %F Icon=/home/pi/FreeFileSync/Build/Resources/FreeFileSync.png NoDisplay=false Terminal=false Categories=Utility;FileTools; StartupNotify=true
Doesn't show up in any of the system menu categories. If I double click the .desktop file, it asks me if I want to execute it.. if I say yes, I get an hourglass cursor for a few moments and then nothing. .desktop file exhibits a generic icon.
Alas, i686 is a different architecture than the Raspberry Pi. The Raspberry Pi runs on an ARM architecture (probably armv7 but I can't remember for sure, and it probably depends on which version of Raspi you're using anyways).
Try searching this forum for the other folks who have successfully compiled FreeFileSync for that architecture.