CPU should be good enough to not bottleneck the setup, well, sadly, FX 6 isn't that good, it'll bottleneck. And almost all MoBos support CFX. It depends on what config do they support it, x8/x4 or x8/x8 (optimal). for $250, you get lot more power than FX 6 or even FX 8, while being cooler and more power efficient, and x8/x4 CFX as well:
CPU: Intel Core i5-4460 3.2GHz Quad-Core Processor (€160.33 @ Home of Hardware DE)
Motherboard: ASRock B85M Pro4 Micro ATX LGA1150 Motherboard (€60.89 @ Home of Hardware DE)
Total: €221.22
For x8/x8 config, you'd be looking at a Z MoBo.
CPU: Intel Core i5-4460 3.2GHz Quad-Core Processor (€160.33 @ Home of Hardware DE)
Motherboard: ASRock Z87 Extreme3 ATX LGA1150 Motherboard (€92.48 @ Home of Hardware DE)
Total: €252.81
Both will support CFX or 270X, but the second one will yield you slightly better results. Why to take AMD when Intel has a better upgrade path and you need to OC FX with an af cooler to match Intel's performance.
PS: Just changed the prices to Euro. And with that budget, you should go for 4690k+ASUS Z97-A and a better PSU.