Peel and cut squash into 3- x 1/2- x 1/2-inch (8 x 1 x 1 cm) strips to make about 5 cups (1.25 L); set aside.
In large saucepan of boiling salted water, blanch haricots verts until tender-crisp, 2 to 3 minutes (3 to 6 minutes for green beans). Drain and chill under cold water; drain well. (Make-ahead: Wrap vegetables separately in towels; enclose in plastic bags and refrigerate for up to 1 day.)
In large skillet, heat oil and butter over medium-high heat until foaming. Add squash; cover and cook, turning twice, until tender-crisp, about 5 minutes.
Add haricots verts, maple syrup, soy sauce, salt and pepper; cook, turning gently, until heated through and evenly coated. Mix in walnuts. Scrape into warmed serving dish.