At the award ceremony for the Grand Prix d’Horlogerie de Genève last November, one winner provoked a few double takes.

The victor among six finalists in the annual design competition’s Challenge category which, last year, focused on watches priced at 2,000 Swiss francs, ($2,203) or less, was the Millesime Automatic Small Seconds, a 39.5-millimeter vintage-inspired dress watch with a steel case and a sector dial, with separate concentric hour and minute tracks.

Its maker? Raymond Weil, a brand making a new play for watch enthusiasts.

Competing against timepieces including a dive-GMT from the industry giant Seiko and a colorful chronograph from the buzzy three-year-old newcomer Studio Underd0g, the Millesime came from a brand that is known more for its affordability and its mainstream appeal than it is for earning the praises of connoisseurs.

Elie Bernheim, 43, is Raymond Weil’s chief executive and a grandson of the company’s eponymous founder, and he was among those who did not necessarily expect the watch to win.

“We had no expectations,” he said in a video call. “It’s something great, absolutely great for us.”

The timing helped to boost the profile of the brand’s wider Millesime collection, introduced this past October. “I don’t want to say that this is the first time that we have so much positive feedback from all the markets,” Mr. Bernheim said, “but it’s not far away from the reality.”