Bring a large pot of salted water to a boil. Add the French green beans and blanch for 3-4 minutes or until tender. Drain in a colander and cover with ice (this will stop the cooking and help keep the vibrant green color). You can do this a day ahead.
Just before serving, heat a large skillet on medium heat. When the skillet is hot add the green beans and tomatoes. Drizzle with the lemon olive oil and season with sea salt and fresh ground pepper. With a tongs, toss the beans and tomatoes, allowing the tomatoes to sear. Transfer to a platter and serve.