From what I understand the Democratic Party in the United States is a wide tent that includes people who consider themselves to be democratic socialists all the way to middle of the road, don’t rock the boat kind of folks. While the former might feel at home in a European social democratic party or perhaps even a socialist party, the latter would likely find more common ground among the liberal (in the economic meaning of that term) or conservative/christian democratic parties.
The main difference I feel is that most European countries have representative democracies with proportional representation in their parliament. This usually avoids the lost vote effect if you vote for smaller parties. Therefore, what are usually the wings of larger parties in the United States, would be separate parties altogether in most European countries.
Having said that the core of the Democratic Party and the majority of people in power and office from that party over the last decade or two have been centrists at heart. Even when given the opportunity they didn’t introduce any true universal healthcare. They didn’t address the fact that the minimum wage doesn’t reflect the rising costs most people face. They didn’t address the rapidly growing inequality. They didn’t move the needle on any public transport infrastructure projects. They successfully kept the country running and the economy growing while not seriously changing anything about the underlying structure of the nation. This is evidence enough for me to assert that the Democratic Party would probably be somewhere around Merkel’s CDU, Rutte’s VVD or perhaps Macron’s party (whatever name it’s currently going by) in terms of ideology.
I didn’t believe that specific rule to be relevant to the argument. The Democratic Party includes a wide range of opinions that, in most European countries, would be represented by several different parties. While there are some fringes on the right (Clinton’s racists for example) and some fringes on the left (some Democrats even refer to themselves as democratic socialists despite being closer to social democrats in my opinion). The mainstream that has dominated all three presidencies you mentioned would likely find themselves among small c conservative or (economically) liberal parties in most European political systems that I know.