Cook haricots verts in boiling salted water until tender, about 4 minutes (or 6 minutes if using green beans). Drain. Transfer to bowl of ice water to cool. Drain well. DO AHEAD Can be made 1 day ahead. Wrap in several layers of paper towels. Seal in plastic bag and chill.
Cut off and discard ends from shallots. Cut shallots lengthwise in half, then remove peel with paring knife. Melt butter with oil in heavy large skillet over medium-high heat. Add shallots and sauté 1 minute. Reduce heat to medium-low; sauté until shallots are browned and tender, about 20 minutes. Sprinkle with thyme. Season to taste with salt and pepper. DO AHEAD Can be made 2 hours ahead. Cover loosely with foil and let stand at room temperature.
Add haricots verts to shallots in skillet and stir over medium-high heat until heated through, about 6 minutes. Season to taste with salt and pepper. Transfer to bowl and serve.