Turn on an LED when power is lost with a relay
If you don't want to bridge the fuse, you can add a relay in series with the fuse. Choose a relay that is closed when no voltage is applied to it (called SPST-NC for Single Pole, Single Throw, Normally Closed) and connect the LED to this relay.

When the fuse blows up, the relay is closed and the LED turns ON. This solution makes sure that your LED circuit is perfectly insulated from the fan circuit.

For example this relay can be used: http://uk.farnell.com/coto-technology/9001-05-02/reed-relay-spst-5vdc-0-5a-through/dp/1079820 

Make sure the current and voltage ratings match those of your circuit, though.