Detection process is pretty straightforward, you just need to browse to C:\ProgramData\Xfire folder (enable viewing hidden items), and change content of xfire_games.ini file for MW3 MP to:
LauncherExe=LaunchIW5M.exe
DetectExe=iw5m.dat
IMPORTANT: Disable Xfire in-game for MW3 MUST be ticked in Xfire options, else game will freeze on start. So, you would need to find alternative for chat while in game. I personally use Steam overlay and chat (game must be added to Steam as non-steam game, and of course, Steam must be running). Also, you need to repeat this every time Xfire updates it's database.
IW5 = the game that IW5M modifies, and the successor to IW4. The only game in the Modern Warfare series to have 3.