Ok!
I'm from Europe too and played this game all the time using several adapters. This game has some issues however, like having a black item screen when you're on the field, a certain scene that sometimes causes the game to crash since the screen (because of the 50hz) can't keep up with the music and the ending always crashes at a certain point. Besides those things the game is nicely playable.
I presume you used this adapter before to play other NTSC games? The point with Final Fantasy III is that it needs some patience to load in an adapter. When it loads you get a black/grey screen first, wait for about 3 seconds and the title screen appears. Although, sometimes it doesn't work. In that case just reinsert the adapter and the game again.
I also found out that the game only tends to work with certain PAL games. I don't really recall which PAL games I used, but I think it was Super Mario World or Super Mario Allstars. Anyway, toy around with those games as well. And be warned, the savefiles of your PAL games could get messed up (or erased) when you use them in an adapter!
Let me know if this worked for you!
One of the adapters I used was this one: http://img451.imageshack.us/i/picture0109bu.jpg/
