Should I apply rigid insulation between existing basement framing?
Here's my preferred basement wall construction method:

Should I use steel or wood studs for basement exterior walls?

You live in NY, so I'm guessing your winters aren't the warmest. I'd suggest pulling out the furring strips so you can put a decent amount of insulation. It's recommended to use a continuous insulation model to a value of r-10:

http://www.buildingscience.com/documents/guides-and-manuals/irc-faqs/irc-faq-basement-insulation

To get to r-10 will take a few inches (it will vary based on the type of insulation you are using...extruded vs. expanded polystyrene, for example.)

Then put up new studs (I'd suggest metal) and then your wall board (I'd suggest a paperless product such as DensArmor).

All that said, if you don't want to go to that extent, sticking 1" foam insulation in the existing cavities will help a bit, so you might as well do it. I'd forgo the tarpaper, though.