WASHINGTON — The Donald J. Trump who turned up in the press cabin of Air Force One on Wednesday evening, as his plane crossed the Atlantic Ocean on the way to Paris, was starkly different from the one who publicly pillories the news media but surprisingly familiar to reporters who know him well.

The president had taken off his tie but kept on his jacket — a wardrobe change that for him qualifies as casual Friday — and he was in a happy-hour frame of mind. Expansive, engaging, even at times ebullient, Mr. Trump held forth for an hour, addressing reporters by name and alighting on topics as different as Chinese history and Julius and Ethel Rosenberg.

It was a loose, good-humored side of Mr. Trump that the public rarely sees amid the fusillade of angry speeches and venomous tweets that have characterized the president’s first six months in the White House. And it came to light only because he retroactively put the session on the record, asking a reporter the next morning why she had not quoted his remarks.

White House aides say they see more of this side in the Oval Office, where the president has debated advisers about issues like sending more troops to Afghanistan. Diplomats say their bosses see more of it in meetings, where Mr. Trump has engaged even those who are deeply skeptical of his views, like Chancellor Angela Merkel of Germany.