I had carpet laid in the basement. I had no intention on finishing the basement, carpet just a place for kids to play. I told the carpet in stallers to leave the carpet enough to frame if needed, well they cut a foot away from wall. Can I frame 1ft away from concrete wall, and if so How do I go about insulation.

Although you will lose the space, you will get better ventilation behind the wall. Frame the wall as usual, pressure treat on the plate. Insulate with batt insulation and put the vapor barrier toward the heated space. An alternative insulation is poly foam in the wall cavity. If you finish the basement, you will need to install wiring for lighting and outlets per code.

If carpet is cut in straight line and equal distance around perimeter, build wall 1'' from concrete wall. Finish area between wall and carpet with ceramic tile or same type carpet with a contrasting color. This will give u a nice border and u will not loss all that space.

If u give a dampness problem, recommend using 2'' poly for insulating. Fiberglass insulation will absorb moisture and loss its insulating power.

Good luck

Chuck