Well, he was ostensibly right in that the US was the dominant power among its Atlantic allies. Does anyone question that? As for "domination", that depends a lot on what one means. The US never militarily dominated western Europe. Perhaps it could have, but then NATO would have looked a lot more like the Warsaw Pact, where the Soviets did precisely that against its own "allies"/satellite states, several times.He complained that NATO was dominated by the US. In retrospect, now that the US in the dominant world power, does his policy make sense? Was NATO used by the US and possibly also the UK to dominate western Europe?
The US did maintain an alliance, and it was the Very Senior Member in all ways. But it was always a hegemonic system, not some kind of satellite system. It's European allies accepted the US' hegemonic status, meaning variable degrees of client-state situations for themselves. In particular over the key strategic issue of nuclear deterrence. The UK got by on its supposed "Special Relationship" (more a Real Thing in London than in Washington) – while the French maintained a somewhat more confrontational partnership.
One of the things the French have always been very keen on is things like the lessons history, in this case Thukydides. They have always recognized that any alliance between partners where a state hands over control of its military to an senior partner sooner or later tends to end up as something other and more unequal than an alliance between equals. (It's also part of why France insists on making all its military gear itself, or as near as.) Part of the problem is that the European dependence on the US for in particular nuclear deterrence has meant it has also been unclear to the US if it maintains an alliance of equals, or if in fact the Europeans are subjects the US and order around? And it has been bad for a lot of the European states as well, becoming reliant on Washington. In the end it has led to Trump's bizarre demands everyone and his granny should pay the US – which would be precisely the kind of relationship the French have always warned about. (Though right now it seems to be Iraq in the crosshairs, wanting the US troops to leave, and Trump making it conditional on them paying him loads of money for the fact that the US is in Iraq since 2003...)
So, during the Cold War it became apparent that no, France in particular was not to be ordered around by the US – and much umbrage was taken. And when push has come to shove post-Cold War, it transpired that for the most part the other US European allies could not be relied on to follow the US off any number of cliffs (Iraq 2003 most starkly) – the GWB neoliberal theory of "billiards" (the US is the biggest ball and so will move all other balls in its direction QED) was disproven, and possible even more umbrage was taken in the US.
Funnily enough during the Cold War, at the Cuban Missile Crisis etc., the French became known as "the foul weather friend" in Washington. De Gaulle was the first US ally to throw in behind the US and Kennedy over the Soviet missile deployment, when it was still completely unclear how the situation might end, WWIII included. So the French might have annoyed the US, but was also known for the fact that when the chips were down they would turn up prepared for war and asking how they could help. (That has subsequently been lost in the post-Cold War US aggravations over the French.)