Maybe the warning light only works with some resistance in the system.
If the system is similar to VW's cold- and warm-diagnosis system for bulbs, the "cold" part works by sending tiny voltage signals through each light circuit upon start-up, whether the lights are switched on or not -- not enough voltage to light the bulbs, but just enough to tell if there's a circuit or not (i.e., burned-out bulb filament).
The "warm" part works by monitoring lights when they're on, to see if current is still running through them. In either case, if something's burned out, the bulb-out warning comes on.
That's with incandescent bulbs and, I think, OEM HID headlights if equipped. It doesn't it works with LEDs; in fact, I've got European LED tail lights on our two VW Mk5's, and I had to disable the diagnosis system on just the tail lights by re-coding so I wouldn't get false errors.
I'm not sure whether the Renegade's diagnosis system is similar; but I'd assume so.
If there were aftermarket LED bulbs in your fog lights, I have no idea how the system would have handled those. Cheap LEDs often cause false warnings.
Anyway, try putting normal halogen bulbs into your fog lights when you get everything back together and see how they work. Please let us know.