I am French, with an understanding of what words actually mean. This article is highly misleading, to be polite. Socialism that has converted to liberal democracy and no longer seeks to replace the market economy is simply not socialism by definition, it's basically social democracy. That's what I have been writing and repeating: It's not because it's called "socialist party" that it is socialist, and that has been the case for decades. Maybe you're too young to grasp this fully.
You think that it's not socialism anymore (which is fair, "socialisme democratique" is not "socialism" anymore), and I say that socialism has evolved ("socialisme democratique" is an evolution of socialism that works in democracies). In the end it's just a difference in the definition.
The fact remains that the US don't really have the equivalent of "Parti Socialiste": the democrats would be on the right wing in France, right?