You may want to make a trip to the big box store and purchase a piece of high density foam insulation board. You should be able to find materials that are colored pink or blue that comes in 1" or 2" thicknesses.
Carefully cut pieces that will fit between the window bottom, side wall and the inward protruding part of the AC unit. If cut correctly you should be able to push the foam material into place with a nice friction fit all around right over those pleated side fillers.
You could also investigate the possibility of cutting a piece that would push in under the AC unit.
It is not clear if a piece would be needed across the top as it is not obvious from the picture if the top area lets in noise to the same degree that the flimsy side pleated panels.
Lastly there is the issue of possible sound coming right in through the AC unit itself. It that is the case this is clearly an issue when the AC unit is off and not in use. So in that case make a cover out of the foam board to put in front of the AC unit when it is not in use. Remove cover to use AC when it's noise probably fully exceeds what external noise that would come through the unit.