“We don’t have much in common.”
Less and less every day.
Rome was way more multicultural. It spanned the whole Mediterranean, all of Western Europe, the Levant, Egypt, the Balkans, Asia Minor, North Africa... Dozens of languages. The lingua franca was not really Latin. East of Tarentum the common tongue and trade language was Greek. Further East it was Aramaic. Elsewhere this was at least a dozen variants of vulgar Latin. And then there were religions.
Latin was an administrative, scholarly language, but even in this role it shared the space with Greek.
for 200 years, the Americans were mostly descended from the Germans and the British stock with African-Americans in the South.
In the past 40 years, that's no longer the case. What is an American? I don't know.
At least in France, they'll demand you to be French and you'll have to adopt their customs which is important for a national identity.