Did you:

1) Download Freelancer Mod Manager and install the mod manager?
2) Double click on the download of TNG, which then "autoinstalls" to the Freelancer Mod Manager directory?
3) Check that the install directory that FLMM will activate over is the correct install path for Freelancer (Options > Choose a different Freelancer directory, and select the correct patch).
4) Activate the mod?
5) Go into your Freelancer folder (Default @ Program files/Microsoft Games/Freelancer/) and go into the Data folder. You should notice some files that are "duplicated", as FLMM makes a backup of files before copying them from the mod. These files will have a filename ending in .ini.flmbak
If you see those files, then the mod has activated, or certainly part of it has.

Have you tried playing the game and seen any changes made by the mod?
If it's just the exe file that has failed to copy across, go into your FLMM directory (default @ program files/freelancer mod manager/mods) and find the TNG directory - inside is an EXE folder, which contains the Freelancer.exe file(version whatever). Copy this file, and then paste it into your Freelancer's /EXE directory. It will replace your existing one (back that up first if you intend to play normal FL at any point ), and change your version number.

Don't forget to permission your firewall if you have one though - it may need repermissioning as FL will have a new version number.