Make the vinaigrette: In a 2-qt. saucepan, bring the grapes and 3⁄4 cup water to a boil over high heat. Reduce the heat to medium, cover, and cook until tender, 10 minutes. Uncover the grapes and smash with a potato masher or wooden spoon. Continue cooking the grapes over medium, stirring, until almost all the liquid evaporates and the grapes just begin to stick to the bottom of the pan, 30 minutes more.
Remove the pan from the heat and scrape the grapes into a fine sieve set over a bowl. Using a spoon, press the grapes through the sieve to yield a purée in the bowl; you should have about 1⁄4 cup. Whisk in the olive oil, vinegar, lemon juice, and tarragon until smooth and then season with salt and pepper.
Line a baking sheet with foil and grease lightly with butter. Heat a small skillet over medium. Add the pumpkin seeds and cook, tossing, until lightly toasted, 3 minutes. Pour the seeds into a bowl and return the skillet to medium heat. Sprinkle the sugar into the skillet and cook, swirling the pan, until the sugar melts and turns amber in color, 3 minutes. Add the 1 teaspoon of butter and pumpkin seeds, season with salt and pepper, and stir quickly to coat. Pour the seeds out onto the prepared baking sheet and spread into an even layer. Let cool completely and then break into bite-size pieces.
In a large bowl filled with ice water, soak the julienned turnips for 15 minutes. Drain the turnips and blot dry with paper towels. Add the turnips to the bowl with the vinaigrette, along with the arugula, and season with salt and pepper. Toss until evenly coated and then arrange on a large serving platter. Sprinkle with the pumpkin seeds just before serving.