Assuming the tensioner is keeping the belt tight, you need to make sure all of the pulleys are still in a straight line. If a bearing has failed in a pulley the puley will "lean" causing the belt to run off the edge.
tensioner wobble , check all pulleys for straightness and replace as need
One of the pulleys is out of alignment,usually it is the tension pully. Replace it and problem will go away.
I would check the serpentine belt and pulleys
Look on the ribbed side of the belt as it is going over pulleys. If you see cracks it would be wise to replace it.
the serpentine belt may be slipping then grabbing as the tranny shifts gears.
You can't, the serpentine belt (or fan belt) on a grand marquis is equiped with a self tensioner, if your belt is making noise it either needs to be replaced or one of the pulleys on the cars may be loose and would need to be replaced.
check to make sure the belt tensioner is functional if not it needs to be replaced
The diogram is usially behind the ratiator if it is not then it would be under the alternator. If you want the Serpentine Belt Routing diagram for your 350 go on www.alldatapro .com.
Start with serpentine belt, then belt tensioner or pulleys, maybe water pump or cam shaft distributor
Without hearing the sound it's hard to diagnose, but I would look at: Alternator, transmission, serpentine belt & pulleys, depending on where the sound is coming from.
Sometimes when a serpentine belt squeals it's because it is too worn or lose to grip the pulleys properly. It could also just be that the tension needs to be adjusted. If the belt is getting worn out, it's best to replace it before you get stranded.
you probably need to replace a serpentine belt or a tensioner. check your belt and pulleys for abnormal wear and proper tension