As I never buy beans in the supermarket, I think what you are looking for is climbing french beans. If you want the very thin ones, then you are looking for filet beans - too fiddly for me. Here in southern scotland I grow 'superbean' Firestorm which is a cross between Runners and climbing french, but tastes more runnery, but then that's what I like. I grow all my beans, dwarf and climbers, inside a polytunnel. Really to choose a variety for your location you need to give various ones a try, perhaps Cobra and Isobel, and see how they do. French beans are very tender, but if you sow them now they will come through after last frost if your climate is anything like ours (minus 4 here last night). Climbing french beans do not like wind, especially cold wind.