Hi everyone !
Here’s the solution for the led usage : just replacing a resistor into 100k and swapping the 0,1uF capacitor for a 10k resistor makes it work.
Since we use the led instead of the lamp, the voltage across this component will be higher since the led draws lesser current.
Thus we need to adjust the voltage divider to the base of the NPN transistor.
Using a 100k and a 10k resistor does the trick !