The French artist painted this artwork in 1874, towards the end of his career. This appears to be a painting of the French military from the end of the eighteenth century, with the soldiers wearing the chenille helmet from the period. The artist was also notable for his paintings of Napoleon himself, as well as the military during the Napoleonic Wars.
The Kunsthalle put it much better than I ever could:
“Meissonier, whose history painting enjoyed great popularity in France, as the early impressionism still met with widespread rejection, presented here six soldiers from the period after the French Revolution. They still wear the uniform of the Ancien Régime, while their helmet already with the badge the Republic is provided. The casual incident on the barracks yard shows a draftsman with a soldier standing in full gear and proud pose model. While the artist and the dog sitting next to him are staring at the sergeant with his saber, four other uniformed men are spellbound in the creation of the sketch. Noteworthy is Meissonier’s finely painted depiction, which impresses with its level of detail and the convincing reproduction of various textures.”