Here's a set of instructions for running FOE on Steam, compiled by motiv.
- Run the FoE installer like normal, changing the install path to xxxx/steam/steamapps/common/rome total war gold
- Ignore the launcher and short-cut prompts, they won't work
- Open Steam, right-click on Rome: Total War Gold in the My Games menu
- Select Properties
- Under the General tab select Set launch options...
- Type in -mod:FOE -show_err -nm (-nm disables the videos and is optional) and click OK
- Launch Rome: Total War Gold by double-clicking it in the My Games menu
- Select Barbarian Invasion from the two-choice list and Launch.