A/C ON: RPM supposed to be higher and aux fan to kick-in?

[StephFR]

My car is less responsive at lower RPM (under 2500 rpm), tipically when starting from stop, only when the A/C is ON.

I understand that the compressor add a load to the engine, but it's really noticeable, like the car having difficulty to get higher RPM up to 2500.

I noticed something strange:

- when I turn A/C on at idle, the engine is not increasing RPM (I thought it was the case on any car to compensate for the load...),

- the auxiliary fan is not engaging: again I thought it should cycle to help A/C efficiency (cooling better its radiator). Car get hotter faster, probably due to that.

Something wrong?
What component is supposed to control higher RPM and fan auxiliary when A/C is ON?