Basement insulation w/ existing tar paper and studs
Building Science Corporation recommends the following model these days for basement insulation:


rigid foam (or spray foam) directly against wall
stud wall (I prefer steel...easier to put up, no mold substrate, really lightweight)
finished wall (I prefer paperless sheetrock again, to avoid having a place for mold to grow)


Note the absence of any vapor barrier...of which tarpaper could be considered one.

The foam board acts as a vapor retarder so it slows moisture movement, but doesn't completely prevent it in case one side has to dry to the other. 

For more details, see my answer on this question: Should I use steel or wood studs for basement exterior walls?