Final answer:
Napoleon hoped to expand his empire's borders and establish French rule across Europe, with the goal of re-creating the Roman Empire under French dominance.
Step-by-step explanation:
Napoleon's hope for each of the different countries of Europe was to expand his empire's borders and establish French rule. He aimed to conquer not just Russia, but also the European part of the Ottoman Empire, including Greece and the Balkans. His ultimate goal was to control Constantinople and the Black Sea, effectively re-creating a new Roman Empire under French dominance.