Assuming it's a modern furnace and not so old it runs off a pilot light ...
No duel voltage systems are common; I've never even heard of one. Essentially, ALL modern furnaces run 120V in North America. It will need that voltage to run not only the inducer motor, but also the fan motor, the circuit board, the ignitor, the flame sensor, and the transformer which steps down to 24vac to run the control circuit).
No single car battery would do. Perhaps a bank of a LOT of car batteries in parallel would work for a while, feeding into an inverter. Not worth the grief, IMO. Go get a generator and wire up a separate secondary dedicated (safety first!) circuit to the furnace. Generally any of the 2000w (or bigger) invertor generators will suffice.