I feel that the 1901 edition of the Almanach de Gotha's blazon of the
arms of the Dukes of Leuchtenberg (
http://gallica.bnf.fr/ark:/12148/
bpt6k309300/f383.image.r=Leuchtenberg.langEN) does shed some light on
the mysterious green quarter with sword and stars, by informing us
that two of the helms have as crest the baton of a marshall of the
French Empire. Combined with the knowledge that seven stars, as in the
Leuchtenberg arms (and the Bernadotte inescutcheon in the Swedish
royal arms) are the symbol of French marshalls and green and gold the
Napoleonic livery colours, we might conclude that Eugène de
Beauharnais was a marshall, but apparantly he never was, was he?