Punishing tariffs on European steel and aluminum remain in place. The administration continues to dangle the threat of duties on European cars, which would be economically devastating for the Continent. Europeans are deeply alarmed by what they regard as the president’s recklessness in the Middle East.

“The current state of E.U.-U.S. relations isn’t good, and I don’t think it’s likely to get better anytime soon,” said Peter Chase, senior fellow at the German Marshall Fund of the United States in Brussels.

Mr. Hogan brings a different set of skills than Cecilia Malmstrom, whom he succeeded as the European Union’s top trade official at the beginning of December. Some in Brussels think his rawer style will make him a better match for the current occupant of the White House.

Mr. Hogan recently said, for example, that by leaving the European Union, the British people were trading in a Rolls-Royce for a used sedan. The statement was seen as particularly cheeky coming from an Irishman who will also be responsible for negotiating a trade deal with Britain as part of its withdrawal from the European Union, a herculean task.

“He is more direct,” said Luisa Santos, the director for international relations at BusinessEurope, an industry group. Gender may also play a role, Ms. Santos said. There is a widespread perception in Washington and Brussels that Trump officials were not comfortable with Ms. Malmstrom, an assertive Swede.