There would be no Catalonian independence movement without the EU. In that case you have two federations (the country of Spain, and the EU) vying for the same territory (Catalonia), which leads to tension. The existence of the EU has led to many such secessionary movements in smaller territories of the larger nations. In Britain, there is (or perhaps now, was) the Scottish independence movement, and to a lesser extent a Welsh one.
Some believed that Brexit would greatly increase the risk of Scotland going independent, and I think that was true, but only in the immediate short-term, while Scotland was still seething from the referendum result. In the long-term, I believe it will reduce the likelihood of Scotland becoming independent. Post-Brexit, we are now seeing the Scottish National Party implode. Is that a mere coincidence? As long as Britain was in the EU, the Scottish nationalist movement could sell the idea of Scotland being an independent member of the EU. Post-Brexit, even if the option was available (there are some doubters, as it would require the assent of countries such as Spain, who have their own secessionary struggles) such a move would place a hard border between Scotland and England. Scotland has an economic dependency on England that dwarfs Britain's on the EU. So if a 'hard Brexit' was an economic catastrophe for Britain, what would it do for Scotland to leave the United Kingdom and join the EU?
Of course, independence is a bit of a misnomer, as true independence is not available, nor sought. In each of these movements, they simply want to change their dependence relationship with the EU. The leaders of the movements gain by receiving elevated status and possibly income, while not taking on additional significant responsibility as would be required for truly independent countries. The desire for power and status without responsibility rather sums up the politics of our age. I believe this is one of the major drivers of enthusiasm for supranational entities such as the EU.