Europe isn't "left" leaning at all. Most of Europe is culturally conservative. It's just like unlike the USA, Europeans believe in strong central governments and even the right usually don't question welfare state.
But it says nothing about Europe and wedge issues like homosexuality, immigration, ...
The fact the far right in countries like France for instance have high voting scores should dispel any sense of Europe being "left leaning".
> Many European countries do not have a political party that is even as right leaning as the Democratic Party within the USA.
This is completely false. Every European country has a far right party, that holds "traditional" view on wedge issues and is opposed to the US made idea of "diversity".
I don't know why americans think Europe is somehow "left leaning", this has never been the case. The divide is more along the lines of "globalists" which are classical liberals and pro EU, and nationalists/isolationists, which are anti-EU, anti-globalism. Both camps have their socially liberal and culturally conservative parties.