Decreasing Noise?

I'm shooting a documentary on a local poet on a 7D and a variety of lenses. After my first round of shooting last weekend, I sat down and discovered most of the footage was ridiculously noisy/grainy. It's obvious that this stems from shooting in extremely softly lit environments (mostly candles and christmas lights).

Is there anything I can do to decrease the noise? I have a small budget and access to FCP studio but can gain access to AE.

Edit: I appreciate everyone's input. NeatVideo has pretty much fixed it. Which is incredible because the video seemed, to me, far beyond fixable. Now, I guess, the question would be if anyone knows how to get for, echem, not $100. Sadly I don't have the budget for it.