When two parties in a trade agree on what is traded, apples for oranges, petroleum for USD, petroleum for EUR, petroleum for apples, and so on, there is no reason why the trade cannot proceed in principle.
If the quote is accurate, it likely means that Juncker is not aware of the practical benefit of having value being exchanged in the form of USD. Since EUR is one of the most traded currencies it imposes a "low" cost in many international trades. Since USD is the most traded currency, more even than EUR, it is likely that on average exchanging USD involves lower costs.
If a French refinery imports petroleum from Saudi Arabia the contract can be in EUR or Saudi riyal or any other currency, in principle, if not in practice. If they use EUR the Saudi company will convert some EUR to riyal and pay a spread and they will convert some EUR to USD and pay another spread. This would happen if the Saudi company needed some American oil field services or equipment. The refinery would get EUR from the sale of refinery products within France but perhaps they would get some EUR by selling GBP following the sale of fuel to a British airline. To sell the GBP for EUR they would pay a spread.
If the EUR spreads add up to more than the spreads that would be incurred had they agreed to use USD in payment for the petroleum then it is less costly to agree to use USD.
If the airline flies many non-U.K non-Europe passengers perhaps they have USD earnings on hand in which case a spread can be avoided by agreeing to trade jet fuel with USD instead of GBP as described previously. This agreement is convenient for the refinery had the refinery already decided to pay Saudi Arabia with USD and of course it is convenient for the airline.
Europeans sometimes pay for European products with USD because one or both parties in the trade may already be transacting in USD for some of their revenues or expenditures. In other words, they tend to receive USD for some of their goods and services or they tend to pay USD for some of their goods and services. If they need to hedge operational risk, the available financial contracts may be denominated in USD so those contracts would make for more perfect hedges if the operations being hedged transact in USD.