Place the halved baby potatoes in a large pot and cover them with cold, generously salted water. Bring to a boil over medium-high heat and simmer until the potatoes are easily pierced with a fork, about 15 minutes. Drain and allow to cool slightly.

Bring a separate pot of salted water to a rolling boil. Add the trimmed green beans and blanch for 3 to 4 minutes until crisp-tender and bright green. Drain immediately and transfer the beans to a bowl of ice water to stop the cooking process. Drain well and pat dry.

In a small mixing bowl, whisk together the extra-virgin olive oil, white wine vinegar, Dijon mustard, creme fraiche, salt, and black pepper until completely smooth and emulsified.

Transfer the warm potatoes and the chilled green beans to a large serving bowl. Add the chopped fresh chives and dill.

Pour the creamy dressing over the vegetables while the potatoes are still warm. Toss gently to evenly coat everything in the dressing.

Let the salad rest for at least 10 minutes before serving to allow the flavors to meld. Serve warm or at room temperature.