1 zecchino of Lombardy-Venetia

Is this coin placed right? It seems that it should be placed in the Republic of Venice under ruling authority of Francis II. Venice was a Austrian province up to 1805 when Francis (II of Holy Roman Empire and I of Austria) gave it to Napoleonic Italy. Catalogue says this coin is from 1815 but that info isn't in coin per se and only temporal info is “Franc.I.”, therefore the coin was coined after 1804 when Franis became monarch of Austria