First, the crash files:
https://www.dropbox.com/sh/ddf30cdewhu74nh/-6144dAocC
The first two are crashes with the tutorial; the 1.31 update fixed that.
However, at various points in a new game, FE stops responding/crashes. The actions were different every time. I am only a few turns into the game; I consider this unplayable.
I'd be happy to help troubleshoot/test.
Finally, I did verify integrity of game cache (Steam).
Core i5-2500K
nVidia GTX 580, latest WHQL drivers (314.07), default profile
(No ATI spam please; this card runs dozens of games without fail and I really don't like ATI)