McDonald’s Corp. failed to win approval to resolve a bitter dispute over claims by franchise employees that they were fired for participating in a national movement for union rights and $15 wages in fast food.

A National Labor Relations Board administrative law judge wrote July 17 that “certain fundamental elements of any effective settlement are lacking.” Such a complicated settlement in a case loaded with confusion and a “history of antagonism” virtually guarantee the accord won’t work, she said.

Critics including Senator Elizabeth Warren had accused the labor board’s Trump-appointed general counsel of trying to railroad workers into a rushed...