Arrange chunks of French bread in a single layer on bottom of pan.
In a medium bowl, whisk together eggs, milk, granulated sugar, brown sugar, vanilla, cinnamon, and salt until fully combined. Pour egg mixture over French bread.
Sprinkle cubed butter on top of French bread. Refrigerate, at least 2 hours, or overnight.
Pour water into Instant Pot®. Place a trivet inside.
Place a paper towel on top of cake pan and tightly cover with foil. Create a foil sling and use it to gently lower pan into Instant Pot®.
Close lid and set pressure release to Sealing.
Press Manual or Pressure Cook button and adjust time to 30 minutes.
When the timer beeps, allow pressure to release naturally for 10 minutes and then quick release remaining pressure. Unlock lid and remove it.
Carefully remove French toast casserole using foil sling. Remove foil and paper towel.