BRUSSELS — When he arrived in the Oval Office for negotiations over their growing trade war, Jean-Claude Juncker, the president of the European Commission, brought a small gift for President Trump, a renowned admirer of military commanders. It was a photograph of the cemetery in Luxembourg where Gen. George S. Patton is buried.

Mr. Juncker, a wily, if often maligned, former prime minister of tiny Luxembourg, added an inscription, alluding to the shared sacrifice of Americans and Europeans during World War II. “Dear Donald,’’ it read. “Let us remember our common history.”

Mr. Juncker left the Oval Office on Wednesday with a deal — or at least a truce — that for the moment has defused the Trump administration’s growing trade war with Brussels, while bringing relief across Europe, especially in Germany. Yet if Europe’s political and business leaders are cautiously optimistic that an economic crisis has been averted, they are also wary, given their history with Mr. Trump in the 18 months since he has taken office.

Even as Mr. Trump cast the meeting on Wednesday as a great success, and offered gratitude to Mr. Juncker, the question is whether the deal represents a meaningful improvement in the severely strained trans-Atlantic alliance, or is simply another example of the unpredictable approach of a president who has spent months mocking and undermining European leaders — even describing the European bloc as a “foe.”