When dealing with Europe and the UK, you can't discount history. Americans often do this because they don't have any history to speak of.
Yes, the fault lines you see do exist, but they are just surface cracks over fissures that go down a thousand years or more.
Simple question: who is the dominant power in mainland Europe? Once, of course, it was Rome, but Rome fell. We had the Merovingians, the Angevins, the Holy Roman Empire, the Spanish. But from the time of Cardinal Richelieu onward, it was pretty much France, right up until Napoleon Bonaparte overdid things and got his ass handed to him. By the time France was back on it's feet, Bismarck had unified the German States into a single nation, and since then, it's been about France vs Germany for European hegemony. Until, that is, Germany was cut in two in 1945.
The French thought they had won. They declined to join NATO, in order not to be compeled to fight Russia to defend West Germany. They established the Common Market/EEC as a method of control and a way to exclude what De Gaulle referred to as 'the Anglo-Saxons' - the UK and the US - from European politics. But then US investment and ther hard work of the German people turned West Germany into an industrial and economic powerhouse. France was forced to let the UK into the EEC in the hope of providing an anti-German back-up. As an EEC and later EU member the UK was uncomfortable, fractious and unco-operative. The stated EU drive for 'ever-closer union' was antithetical to the bloody-mindedly independent people of our foggy little island.
Then Germany was re-unified, over strdent French appeals for caution and delay. Shorn of its economic dominance, and ill-served by an increasingly uninterested UK, France had only its' military superiority over Germany left. Germany had avoided re-armament because they knew it would cause a panic in other parts of Europe and in Russia.
Now the UK is out of the EU, and it's between France and a newly-rearmed Germany again. Both countriues are convinced that they are or should be dominant in Europe. Both sides are convinced the other is unremittingly hostile to them. That same, ages-old rivalry -whatever modern form in manifests itself as - is what will tear the EU apart before the end of this century.
Russia, in its current form, may well not survive the ongoing debacle of European adventurism. The US is perilously close to some kind of implosion - either a radical change or a total collapse. The disappearance of any viable rival will terminally undermine China. Climate change and viral pandemics will probably reduce the human population by at least two-thirds. It will be a very different world you and I will probably not live to see!