I'm in the same boat here, GTX960 4GB, i5, 8GB RAM, no difference between high or low settings, frame rate is still between 15 - 20FPS.
I have another PC that runs on high, with no issues on a GTX 680 2GB. I have tried VSYNC on/off, uninstall, update, graphics drivers. I have tried older drivers, I have tried turning off the Origin in game option. Nothing is working so far. This issue was not always prevalent though as I had the game running at ~100FPS on high settings before January, something happened in Jan, then boom.
I have tried other games also (Arkham City, Crysis 3, Far Cry 4, etc.), high settings, no frame issues at all.