Have an NPN after the fuse, and LED powered from before the fuse.
When powered, the NPN will be on and is used to pull the LED anode low.
When the fuse blows, the NPN turns off and current is allowed to flow into the LED to light it up. Put the LED current limit resistor between the supply and the anode, and the NPN collecter to the anode, with emitter to Gnd. Fused power goes thru resistor to NPN base.
True, power will still be active when the fuse blows; mount the current limit resistor close to (right at) the supply, so only a few mA can flow no matter what (thru the NPN, or thru the LED).