Well if you want to keep it really simple, you could achieve an inverted logic(led off when fuse is okay and on when fuse is blown), you could simply connect the led circuit in parallel to your fuse.
Your led circuit would be simple, your LED in series with a higher reverse voltage diode(something like 1n40007 could work) and a resistor. Your led, the diode and led would all be in series and would typically stay off if the potential difference across the fuse is 0v(fuse is intact). The potential difference would rise to line voltage when the fuse is blown and hence your led would light up. You may find a bit of flicker in led due to line voltage frequency but It shouldnt be a major challenge.
If you certainly want the led to be on while your fuse is intact, you would have to wire up the led circuit between live and neutral. The led, diode and resistor would be connected between live(live after fuse) and neutral. From an execution perspective, solution 1 would be simpler to wire up and execute.
Hope this helps.