Air Fryer Beignets. The term beignet refers to a French-square doughnut. You cannot visit Louisiana without trying beignets; after all, it has been the official state doughnut since 1986. In the 18th century beignets were brought to Louisiana, we enjoy this light, fluffy pastry with powdered sugar, thanks to the French Acadians. To make the beignets healthier, we used gluten-free flour and made them vegan. You can taste Louisiana in your kitchen whenever you make these air fryer beignets.