OK, so you have the Athlon version of the A10-6700 chip (FM2 socket). Of the Borderlands 2 CPUs (http://www.techspot.com/review/577-borderlands-2-performance/page6.html), that's probably going to end up around the Athlon II X4 645 in performance. The GTX 960 is roughly comparable to the GTX 680 they tested with (http://www.anandtech.com/bench/product/1494?vs=1596, http://www.tomshardware.com/reviews/gpu-hierarchy,4388.html).
So, if anything, I would expect you to be getting 30-40FPS @ 1080p resolutions in that game, based on the CPU & GPU combination you have.
There's not a whole lot more you can do CPU-wise with that system -- maybe trade it out for an FX-770K or an Athlon X4 880K (depending on which would be available), but that's assuming your motherboard can handle it -- the latter being FM2+ CPUs, which may or may not be compatible with your board. Again, depending on the board you might be able to OC your current CPU with an aftermarket cooler, but there might not be a whole lot you can do with that.
If you're concerned about the FPS, experiment with your settings & resolution, starting off with increasing the resolution & quality (if possible). Since that dumps more of the workload onto the GPU, you'll probably see little to no change in your performance if your CPU is in fact holding you back. If that doesn't work, try turning down the details & resolution to see if you get an FPS boost.