PARIS—French restaurant owners and workers are as worried as anyone about the coronavirus—but they’re also concerned that new mandatory COVID passes will turn them into virus police instead of purveyors of culinary pleasures. Starting next month, all diners in France must show a pass proving they’re fully vaccinated, or recently tested negative or recovered from the virus. For restaurants—seen as the lifeblood of France—the new rule presents yet another headache after a punishing pandemic. “Our job used to be to make sure that our guests had a great time while they were with us. Now, we spend our time reprimanding them. We weren’t trained for this,” said Louis le Mahieu, manager of the Parisian restaurant Les Bancs Publics. Les Bancs Publics sits on a street corner on the canal that wends through northeast Paris, a neighborhood popular with young people who gather in its many cafes or on the banks …