Looks quite good, I think The ideas are all a bit crazy though.
An officer might be dressed and armed a bit like that, or perhaps an elite unit like marines (with a pistol instead of the rifle), but for the bulk of napoleonic era troops, being armed with two expensive weapons would be totaly extravagant. The whole idea of nationalistic 18th century armies is that people are cheap, while weapons and horses are expensive.
That doesn't mean I think its a stupid idea, but I'd go for two units, one rifleman, and one elite trooper/marine (Because of Rome's position within the mediteranean they would likely have a large navy had they survived to that time). The elite trooper would be a bit like Kinboats man at arms, with a sword and pistol, and very extravagant volouminous clothing, or lots of exposed flesh, in a short toga style garment with dashing short cape... Being an elite soldier after all would be very much about getting all the chicks! The main thing is that much of thier outfit would evolve from civilian fashions, along with mixed influences from adjacent civs.
Take the frock coat for instance, which was a large part of european armies uniform. It was originaly influenced by middleastern fashions, and was taken up by civilian proffesions like doctors or bankers, and also became part of military colthing.