Can I remove the framed wall on the outside of my basement?
The 2x4 wall is certainly not load bearing in terms of the floor joists, etc.  The floor joists will be supported by the concrete walls, and possibly by a beam or wall somewhere along the span.  Since the wall in question is right next to the concrete outer wall, it won't be supporting the joists.  If the ceiling isn't finished you can likely see for yourself that the ends of the joists extend out over the concrete wall.  

If a mid-span wall is supporting the joists, it should have a double top plate, and king studs around doors and such.  Otherwise, it is likely just a non load-bearing dividing wall.  You can also measure the joist depth and length and compare to span tables to see if a mid-span wall is likely to be load bearing.  If you have TJI joists (OSB web with laminated top and bottom) it may be a little more difficult to identify your joist.

If you have a suspended ceiling or such, it may be involved with this wall.  And you might have wiring or plumbing in it.  But it's not holding up the house.