This is almost entirely backwards.
European liberalism is the wellspring of American liberalism, but Europe has - for obvious, historical reasons - much better organised reactionary elites. The equilibrium between the European publics and elites does indeed wax and wane.
In the 1990s a whole bunch of elite shibboleths were encoded into supranational law (so that no elected government is able to repeal them) as incredibly vaguely defined "human rights", which in turn have given rise to a vast bureaucratic apparatus to administer them (often staffed by the children of elite families). This apparatus is used as a cudgel to chip away at basic liberties - abstract, ill-defined communitarian rights (eg "safety") are used to sweep aside actual, tangible individual rights (eg speech, privacy).
(As an aside, the Soviet Union did effectively the same thing with their emphasis on "social rights" - such as those in the ICESCR - as opposed to "bourgeois" individual rights - such as those in the ICCPR. Didn't work out great for Soviet citizens.)
Since the 1990s, as a result of misgovernance by its chronically incompetent elites, Europe has been in decline by almost every metric. In the past ten years or so, the European publics have been in increasingly open revolt about this. A bunch of populist opportunists have seized on this revolt to offer various alleged alternatives, but been unable to deliver any sort of tangible change. (There is no reason to believe any change will come from this group, since they are basically just the second-rate members of the existing elite who have bet on populism as their ticket to the top.)
Europe tells itself stories about being a "human rights superpower" as an adaptive mechanism for its clear decline in prosperity, freedom, and relevance.
IMHO, Europeans deserve much better than this sad, managed decline. But given the deep structural barriers to protect the elites and prevent change, I just cannot see how this gets better.
Will the last European please turn out the lights?