If we’re talking about etymology, the term “left-wing” did indeed originate from French politics and designated political movements by where members sat in the French National Assembly. So, not originally American as you stated. But the etymology aspect is not really all that interesting.
In terms of ideology, placing americans at the origin of everything is revisionism. Left-wing ideology is mostly descended from the thought of mostly European philosophers from the Age of Enlightenment.
I can imagine a mutual game of influence that goes both ways, but to claim that Americans invented it all is a bit of a stretch.
I did acknowledge that there was influence (that goes both ways). But saying one stems from the other is still wrong, and I rest my case: the US are not the center of the world. There was a world before, and there will be one after its collapse, whether you like it or not.