Pour 2 tbsp olive oil into the Instant Pot.
Select the Sauté function and allow the oil to heat.
When the oil is hot, place the chuck beef roast into the Instant Pot.
Sear the roast for 5 minutes on one side.
Carefully turn the roast over and sear for an additional 5 minutes on the opposite side.
Pour the beef broth into the Instant Pot.
If needed, gently scrape the bottom of the pot to loosen any browned bits.
In a large ziplock bag, combine the baby carrots, chopped yellow onion, quartered baby red potatoes, French onion mix, and remaining 2 tbsp olive oil.
Seal the bag securely.
Shake the bag until the vegetables are evenly coated with the oil and seasoning mix.
Evenly distribute the coated vegetables around the roast in the Instant Pot.
Secure the Instant Pot lid.
Ensure that the steam valve is set to the sealed position.
Select the Manual or Pressure Cook setting.
Cook on high pressure for 70 minutes.
When the cooking time is complete, allow the pressure to release naturally for 10 minutes.
After 10 minutes, carefully perform a quick release to release any remaining pressure.
Once the steam has fully released and the pressure pin has dropped, remove the lid carefully.
Transfer the roast to a cutting board or serving platter.
Shred the roast using two forks.
Remove the carrots, potatoes, and onion from the Instant Pot.
Serve the shredded roast warm with the cooked vegetables.
Spoon additional cooking liquid over the roast, if desired.