As the Republican primaries drag on, some of Mitt Romney’s old friends are harking back to a time when, decades ago, the former governor honed his skills at winning over skeptics. That time was 1968, and the place, France, where Romney was stationed as a Mormon missionary. While the issue at that time was Romney’s religion, rather than his politics, his old friends say that Romney’s long slog to win delegates state by state bears some resemblance to the challenges he faced as a missionary in France, where every conversion was hard-won.

“It would be an understatement to say we were not universally loved,” says Dane McBride, a physician in Roanoke, Va., and one of Romney’s fellow missionaries in France, who remains a close friend and...