Mr. Juncker grabbed the opportunity to argue that both sides need to refrain from further punitive tariffs or they would foolishly harm themselves.

“If you want to be stupid,” he told Mr. Trump, “I can be stupid, as well.”

Backing up his points, Mr. Juncker flipped through more than a dozen colorful cue cards with simplified explainers, the senior EU official said. Each card had at most three figures about a specific topic, such as trade in cars or standards for medical devices.

“We knew this wasn’t an academic seminar,” the EU official said. “It had to be very simple.”