What was the most elite military unit at the time of the Napoleonic Wars?

In short answer, it should be the Imperial Guard of Napoleon Bonaparte, especially the Vieille Garde or the Old Guard.

Napoleon’s Old Guard consisted of several grenadier, chasseur and heavy cavalry regiments (Grenadiers à cheval). Most of its members were the very experienced officers and soldiers with at least ten years of service. Until 1810s, many of them had started their military careers for more than twenty years since the days of the French Revolutionary Wars (1792–1802).

Undoubtedly, the Napoleon’s Old Guard earned its fearsome reputation as one of the most elite units of the Grande Armée. They fought with extraordinary bravery against all opponents of the French Army: the British, the Prussian, the Austrian and the Russian armies, with remarkable successes.

Spring 1807, on the field of Preussisch-Eylau where the snow was covered by blood and the land was littered with dead bodies, under the terrible cold and the intense Russian artillery bombardments, the Grenadiers à cheval of Napoleon’s Old Guard participated in one of the greatest cavalry charges in history. Fifteen thousands French cavalry sabres finally stopped the Russian advancement and successfully saved the reputation for Napoleon with a Pyrrhic victory.

Winter 1812, on the field of Krasny in Russia, the Old Guard fought valiantly to protect Napoleon and his general staff from the attacks of the Cossack and the partisans. Denis Davydov, a notable Russian partisan leader who organized this famous ambush against Napoleon Bonaparte and his men, also wrote some meaningful comments about the Old Guard in his memoirs as follows:

”...After midday, we sighted the Old Guard, with Napoleon riding in their midst... the enemy troops, sighting our unruly force, got their muskets at the ready and proudly continued on their way without hurrying their step... Like blocks of granite, they remained invulnerable... I shall never forget the unhurried step and awesome resolution of these soldiers, for whom the threat of death was a daily and familiar experience. With their tall bearskin caps, blue uniforms, white belts, red plumes, and epaulettes, they looked like poppies on the snow-covered battlefield... Column followed upon column, dispersing us with musket fire and ridiculing our useless display of chivalry... the Imperial Guard with Napoleon ploughed through our Cossacks like a 100-gun ship through fishing skiffs.”

(Denis Davydov, In the Service of the Tsar Against Napoleon: The Memoirs of Denis Davidov, 1806-1814, Greenhill Books, 1999, p. 142)

Undoubtedly, the Napoleon’s Old Guard was extremely powerful like a 100-gun ship-of-the-line shattering through the Cossack and partisan formations! During that day, Davydov and his men captured seven hundred French prisoners of war, however, none of them was the Old Guard!

The Old Guard continued to gain their fearsome reputation during its final fight: The Battle of Waterloo (1815). In August 1815, the new regime of King Louis XVIII ordered the Imperial Guard abolished. Since then, all formations of the Old Guard and the Imperial Guard in general were disbanded, their officers and soldiers finally became the war veterans.

However, the reputation of the Vieille Garde or the Old Guard as one of the most elite units of the Napoleon’s Army has become something immortal. Once again, thank you very much for reading my answer and best regards,