Interestingly, the American roots of free speech come from across the Atlantic. Milton's Areopagitica, J. S. Mill, and Voltaire all contributed to the American foundations on this topic. The Constitution was written in light of centuries of European powers using speech restrictions to punish dissent. After the revolution, Americans continued to be influenced by European thinkers, like Kafka and Sartre, or Émile Zola who was punished with criminal libel for exposing antisemitism. We followed with sadness and hope the emergence of samizdat, the attempt to share ideas under yet another authoritarian European regime.
These European thinkers have not always aligned with European policy. You cite Nazi Germany as the result of free speech, but it is an odd example. The Gestapo arrested people for things like "listening to the BBC" or "attending a party where someone made a stray remark about the course of the war."
I take your perspective as, "we must stop Nazis early before they come to power, and limiting public speech is an effective tool to do so."
You probably think of governments restricting speech more along the lines of Germany restricting holocaust denial, but Poland uses the same framework to restrict the acknowledgement of the Polish role during the holocaust.
The US perspective is just that inevitably you're going to get some bad governments, and they will use speech restrictions to suppress counter-speech that is necessary to bring things back to normal. And that driving speech underground isn't really an effective way to stop it.
The question for us is not, "is there some speech you would like to restrict?" But "would you like to allow your political opponents to control your speech?"
You're right that there's a difference in perspective. I know this debate can be frustrating from either side, it draws on intense conviction. But if you're passionate about it, it's worth understanding the roots of it, and knowing that Europe has not been monolithic on this issue.