In a wide, shallow bowl, whisk together the eggs, pumpkin puree, milk, vanilla extract, maple syrup, pumpkin pie spice, and salt. Continue whisking until the mixture is smooth and the pumpkin is fully incorporated into the liquid.
Preheat your air fryer to 375°F (190°C). Lightly grease the air fryer basket with cooking spray or a small amount of melted butter to prevent the bread from sticking.
Dip each slice of bread into the pumpkin custard mixture. Let it soak for about 15-20 seconds on each side. You want the bread to be well-coated but not so soggy that it falls apart when you pick it up.
Place the soaked bread slices in a single layer in the air fryer basket. Do not overlap them; you may need to cook in batches depending on the size of your air fryer. Cook at 375°F for 5 minutes.
Open the air fryer and carefully flip each slice of French toast using a spatula. Cook for an additional 3 to 5 minutes, or until the edges are golden brown and the center is set.