Most oil exporting countries trade assets in USD, meaning, these countries receive a significant portion of USD inflows from the proceeds of these sales. Thus the foreign currency reserve balances of these oil exporting countries, in a sense, is broadly reflected by the price of oil. We can see this as reflected in the chart below. Up to 2014, reserves increased notably, and then declined considerably as the price of oil fell.
However, data also shows that they invest part of their reserves in EUR, as they sell a large share of their production to the Eurozone.
Thus, when the price of oil falls, this means that a smaller portion of USD is transferred to EUR, thus contributing to a depreciation of the currency. Inversely, when the price of oil increases, a larger portion is transferred to EUR, contributing to the appreciation of the currency. For this reason, many funds lock their positions in EUR/USD with those in crude oil.
Therefore, it is no coincidence that COT data shows crude oil and EUR in lock step.
Hope this helps!