In a large bowl crack two eggs and beat thoroughly.
Add both white and brown sugars and continue mixing.
Add milk, pure vanilla extract, and cinnamon.
Beat until all ingredients are combined.
Place a large skillet over med-high heat and add unsalted butter.
Dip slices of bagels into the French toast batter and shake off excess batter.
Place bagels cut-side down into the skillet and cook until golden brown. Flip over and continue to cook until side is golden brown.
Remove from the skillet.
Add cooked peaches and plums.
Serve.