The message of Ingres painting conveys is that Napoleon was a fundamentally imperial individual and the heir of Charlemagne. The dress choices were not accidental, but were in keeping for an individual of his status. The Ingres painting blends both ancien regime motifs and the symbolic language of the new regime.

The cross around his necklace is the Légion d'honneur, signifying that he is the ultimate creator and arbiter of this imperial institution. The award was open to all individuals that served the French state. Although there had been other chivalric orders in European history such as the Order of the Garter or the Golden Fleece, but the French Legion, instituted by Napoleon was more meritocratic and open compared to its predecessors.

The coat with black spots is a hood of ermine, also known as a stoat, which was the fur of choice to connote the bravery of the monarch. The stoat is not only a relatively rare animal, but legend has it that it would rather die than surrender. The sword and scepter were those of Charlemagne. The hands on the scepter were ivory and were symbolic of Charlemagne's hand of justice. Napoleon would often draw explicit connections between himself and Charlemagne. He would say:

I am Charlemagne; for, like Charlemagne, I have united the French crown with that of the Lombards, and because, like his realm, my empire stretches all the way to the Orient. I expect people to keep that in mind in their dealings with me.

One of the curious side stories of the Napoleonic era was that his imperial genealogists tried to connect the Bonaparte family to the Carolingian dynasty.

The bees were the heraldic symbol of the Bonaparte family, and again were a conscious choice on the part of Napoleon. The bees are both industrious builders but also fierce on the attack. The eagle at his feet is the imperial eagle of the Napoleonic state. The eagle was the standard of the French armies and a reminder of one of the pillars of his support. The laurel wreath is Roman, also signifying that Napoleon was an emperor and not just a mere king.

Thus the painting is a fusion of both the contemporary French empire and that of a bygone age: the era of Charlemagne. H. G. Wells once said of Napoleon, "he could have been the father of a new world, but chose instead to be the stepson of the old." However, Napoleon's styling was often reaching back further than the Bourbons masters of France. Napoleon aspired in many ways to create a pan-European imperial order, one that was culturally French, but also beyond the borders of France. The opulence of the Ingres painting reflects this imperative.

Edit: accidentally hit enter before done

Sources

Nora, Pierre. Rethinking France = Les Lieux De Mémoire. Chicago, IL: University of Chicago Press, 2001.

Nouvel, Odile, and Anne Dion-Tenenbaum. Symbols of Power: Napoleon and the Art of the Empire Style, 1800-1815. New York: American Federation of the Arts, 2007.