I actually see two potential issues here. When you say "two breaker switches", do you mean two separate single-unit breaker switches? Or do you count a double-slot two-pole switch with a handle tie between the two switches as one unit and call it "one switch"? Either way, it is either rather unusual or simply wrong setup. The electrical furnace is a very high power appliance (8-10kW at the minimum) and it should be on a 3-wire 120/240 volts single-phase service which has two live wires to increase its current capacity. So the double pole breaker is designed to trip and disconnect both live wires in the event of over-current on either one of them.
The furnace is internally wired to use the current from both live wires and would sort of limp along at about 1/4 of its capacity if one of the live wires is disconnected. The blower in the air handler that is pushing both hot and cold air through is most likely connected to the breaker of the outside A/C unit (yet another two pole breaker you would normally see in the panel) and that's why the A/C keeps working.
Anyway, I just wanted to point out that if you have two breakers labeled "Furnace", you have to have them as a single action two-pole breaker with a common trip. Otherwise you may disconnect only one of the live wires feeding the heating element and it will still be energized through the other one and someone can get hurt.
Oh, and the other potential issue I was talking about is that the furnace was not properly wired from the beginning and was probably constantly consuming the 2kW during its entire lifetime. I would need to know more about the furnace (model #, approx. year) and your confirmation about the circuit breaker type to dig deeper into this. But in the end it may require a repair that's best left to a professional HVAC technician anyway.
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