My initial guess, as confirmed by the Louvre web page for the painting, is that the figure is a chasseur à cheval of the Imperial Guard, who wore hussar-style uniforms (and rather distinct ones at that) rather than the more subdued chasseur-style ones. You can see their uniform in this uniform plate by Knötel.

The tan/buff-colored breeches are the giveaway; I've only ever seen the guard chasseurs depicted with them, and they're described as part of the uniform, for example, in Smith's Armies of 1812.

As to why they have a hussar uniform despite being chasseurs, it's worth noting that under the Republic and early Empire chasseurs did wear hussar-style uniforms, albeit simplified, as in this illustration by Lienhart and Humbert.