Put the potatoes in a pot of generously salted water and bring to a boil over high heat. Boil until the potatoes are just tender, about 8 minutes. Drain and cool slightly, then cut the potatoes into quarters.
Heat a charcoal or gas grill to medium-high.
Toss the potatoes with a little canola oil and season with salt and pepper. Put the potatoes in a grill basket and grill, covered, tossing and turning occasionally, until lightly charred in spots, about 5 minutes.
Transfer the potatoes to a bowl and immediately add the vinaigrette. Put the arugula on top and scatter the goat cheese over the arugula. Season with salt and pepper. Quickly and gently fold the mixture once or twice to combine. Serve warm or at room temperature.
In a medium bowl, whisk together the lemon zest and juice, mustard, tarragon, honey, and a little salt and pepper. Slowly whisk in the olive oil until emulsified.