Arrange the potatoes on a baking sheet and lightly spray with olive oil.

Bake until golden and crispy, about 30–35 minutes, flipping halfway through if needed.

Season immediately with salt after removing from the oven.

In a small saucepan, combine the shallot, white wine, champagne vinegar, and 2 sprigs of tarragon.

Bring to a simmer and cook until the liquid reduces to approximately 1½ tablespoons.

Strain the mixture and set the reduction aside.

Melt 6 tablespoons of butter.

Add the egg yolks to a blender. With the blender running, slowly stream in the melted butter until emulsified.

Add the remaining room-temperature butter and blend until smooth and creamy.

Stir in the reserved reduction, remaining chopped tarragon, and salt to taste.

Generously season the beef tenderloin with salt and pepper.

Allow the steak to rest at room temperature while preparing the remaining components.

Heat a skillet over medium-high heat.

Sear the tenderloin for approximately 3 minutes per side, about 12 minutes total for medium-rare.

Transfer to a cutting board and let rest for 10 minutes before slicing.

Arrange the sliced beef tenderloin alongside the crispy fries. Spoon the warm béarnaise sauce generously over the steak and serve immediately.