An 8400 @ 3.4 will draw what, 100-120W?
And the GPU slightly more than a 100W? Up to 140 under Furmark.
So a hypthetic decently specced 250W PSU would be just about enough.
Whether or not 12V has enough amps on the offer, depends from PSU to PSU - these days most PSU's offer around 95-100% on 12V. If a PSU doesn't, it's highly suspect.
PCIe connectors can be easily bought after-market and plugged onto two molex 4-pins. They're not magic in any way.
So while in the extreme case, of a hot OC, and furmark, a 250W PSU might be running at 105%-110%, that's within tolerances for most well-made PSUs.
A 350W 80+ Gold or Platinum is probably the safest bet. Sadly, below 350W there isn't much to be fund with regard to quality ATX PSUs. I recommend Seasonic, FSP or Enermax, in that order. Better to go for an expensive "small" PSU, than a cheap "big" one, simply because it gives you better protection for the built-ins, less fire risk, better efficiency at idle (where most non-gaming usage puts you) and partial loads, less noise and longer life span. Paying more for less Watts usually makes sense.