Democratic Party voters seem to be more aligned with Euro-style socialist policies, but among elected Democrats this is a small minority view.

European socialists usually advocate for direct state ownership of certain industries, sector-wide union contracts, universal (not means-tested) child allowances, fully public health care, wealth taxes, free college, etc. There are a handful of elected Democrats that sign on to some of these views, but these have never been in the actual party platform, since the mainstream of the party roundly rejects these. Democrats are only somewhat radical in certain social/bioethical issues like abortion and LGBT rights (although the latter is being tested, with some influential Dems defecting); otherwise, the better European analogue would be Macron's Renaissance party (formerly En Marche), the UK's Lib Dems, the Nordic countries' social liberal parties.

I don't think there's particularly good alignment even on that "axis" (it isn't really an axis, because most things are not inherently one or the other.) A good example of that is the "sector wide union contracts" thing. The default "leftist" position in the US is that things that apply to an entire sector should be legislated rather than negotiated by workers

The US does have child allowances, by the way - during Covid, it was even increased and paid out monthly instead of annually. Increasing it as of late seems to be an "R" policy, at least on the Trump wing.

Are there European countries that offer free college regardless of academic achievement during high school?