Bring a large pot of lightly salted water to a boil. Cook green beans in boiling water until crisp-tender, about 4 minutes; drain. Plunge beans into a bowl filled with ice water to cool; drain beans.
Combine red wine vinegar, rice vinegar, ground ginger, sesame seeds, sesame oil, soy sauce, garlic, and sesame seeds in a bowl. Whisk canola oil into the vinegar mixture until thoroughly incorporated; season with salt and black pepper.
Toss green beans, grape tomatoes, and shredded carrot in a large bowl. Drizzle dressing over the green bean mixture; toss to coat.