I have asked this question before, but I believe it is allowed to repost when you do not get any replies, so I will try a second time: They wear them on every picture and in every game I've seen for the period. I have come to wonder whether they had a practical use, because it seemed weird and expensive to issue them for every soldier if it had no use. Did it help protect them? Signify their rank? Or did it otherwise come in handy? If it was for pure display, then why was that so important that you would spent so many resources on it?
The top hats were called shakos. The tall feather you are referring to was known as a plume. Seen here and here.
Plumes were more of a fashion statement, never worn during battle or on campaign. They were supposed to be worn only by senior officers, but found their way onto the shakos of Grenadiers and Voltiguers, even a few Fusiliers worn them. These were mainly wore during parades to make the soldiers look sharper.
Beneath the plume there was a small colored ball called a pompon. Pompons were part of the standard uniform and were worn without the plume attached during campaigns. They signified which company a soldier was assigned to:
Red - Grenadier
Yellow - Voltigeur
Green - 1st Fusilier
Blue - 2nd Fusilier
Orange or Pink - 3rd Fusilier
Violet - 4th Fusilier
Shakos also had braided cords that again signified the soldier's company.
Red -Grenadier
Yellow/Green - Voltiguer
White - Fusilier
