FF I–VI weren't released in Europe. The first FF game released here was VII. But generally I think the popularity of FF games in Europe is similar to that of the US.
If I remember correctly, a lot of people were asking (on Facebook, etc.) why they don't have FF VIII and IX in the first Final Symphony. I think that might be one reason those two games were included. FF XIII is a natural choice, since Hamauzu is involved in these concerts. FF IV is more popular in the West than FF V, but not in Japan, I think. I actually like that they included V instead IV, because it's more unexpected.
I agree, however, that IV and XII deserve a concert treatment (especially a Valtonen/Wanamo treatment!). I can't see a FS III without those games and the team would gain eternal respect from all those XII music fans (myself included). I'm sure IV would be a blast for Wanamo or Valtonen to arrange, since it's classic retro Uematsu with lots of quality melodies. But XII is a challenge because it's already so orchestral. How do you make an orchestral arrangement of orchestral music, that is different and interesting, but doesn't upset the listener because there's a violin instead of a flute for that beloved melody? Valtonen and Wanamo said something like that and thus prefer arranging music from retro games.
I do think FF VI–X are the most popular and draw the biggest crowds in Europe (just a gut feeling, what do others think?). So in that sense they have "used up" the best games. But Final Symphony has gained a good reputation, so I'm sure they would sell out with other FF games as well. I've never heard anyone say anything bad about FF IV music and it's still a big card to play.
I can't help but think that FS III would be a great opportunity to give tribute to Sakimoto with half a concert (XII and Tactics). Though business-wise FF XV would probably draw crowds, if it's out by then. They could also consider FF VI, since it still has lots of material to work with (character themes, Dancing Mad...) and Wanamo loves its music.