Why did Napoleon III use aluminum silverware?

He didn't use aluminum silverware. Aluminum objects were not produced in his life. He died in 1873.Most likely he used tin. It isn't until the late 1889 that a process was developed by Charles Martin Hall to make it into objects. As early as 1787 the ore was known to exist, but there was no way to extract it until 1825.

___

Yes Napoleon III did use aluminum utensils. He was very proud of them.

"Napoleon III proudly displayed aluminum cutlery at his state banquets, commissioned aluminum equipment for his military and even had an aluminum and gold baby rattle made for his son."

Henri Sainte-Claire Deville of France discovered the aluminum process prior to the American discovery. Charles Martin Hall and Frenchman Paul L.T. Héroult discovered a cheaper way of making aluminium.