There are 2 fans that can be considered as A/C fans, one inside the car which is also shared with the heating system, and the radiator fan which is turned on constantly when the A/C is set at max cooling. Normally when the radiator fan goes bad, or the mount for the fan gets damaged, You notice it when the A/C is first turned on.
The fix for this is to replace the fan, or the radiator support, which means the complete front end of the car (radiator support) needs to come off. A second method is to leave the broken fan in place and add a second fan in front of the radiator pak, wiring it in the current fan wiring and run that one. It takes much less time and effort, but requires a bit of fabrication to mount it. I have done this on a few cars with much success. When done, you can't see the change and it is perfectly silent. Cost for the aux fan is around $70 and about an hour or so of labor.
If the fan noise is inside the car, (blower motor) and it only makes noise at a specific speed, the fan can be removed by a simple disconnection of the wires, and pressing a plastic tab,rotating the motor slightly and it comes out. Located just above where your foot sits on the gas pedal. Could be something fell in the housing, or a damaged fan blades. easy replacement. If it doesn't work at all on one speed setting, it also could be a resistor pack, which is also located near the blower motor.