Check your folder structure (I had an extra folder as a result of unzipping, which interfered). Looking down the path from OpenXCOM folder, you should have "user", then "mods", then "Final Mod Pack", that folder should then have all of the various folders from FMP. Actually, from what you said, I think your "mods" folder is too high, move it down inside "user".
Then after you launch the game, go to Mods button from title screen, the Final Mod Pack should be one of the last entries, activate it, when you press OK, game should restart and the title screen will say Final Mod Pack.