Start by trimming the ends of the haricot verts and rinsing them well. Bring a pot of salted water to a boil and blanch the beans for a few minutes until they are just tender. Drain and immediately rinse under cold water to stop cooking and preserve their vibrant color.
In a large skillet, heat butter and olive oil over medium heat. Add the finely chopped shallots and cook until they become soft and translucent. Stir in the minced garlic and cook briefly until fragrant, being careful not to burn it.
Pour in the chicken broth and let it simmer for a minute to reduce slightly. Add the heavy cream and Dijon mustard, stirring continuously to combine everything into a smooth, creamy sauce. Let it simmer gently until it thickens.
Add the blanched haricot verts to the skillet and toss them in the sauce. Make sure each bean is well coated with the creamy mixture. Allow them to cook together for a few minutes so the flavors fully blend.
Taste the dish and adjust salt and pepper as needed. Once everything is heated through and well combined, remove from heat and transfer to a serving dish. Serve immediately while warm for the best flavor and texture.