If a recipe calls for "French cut" green beans, it simply means the beans are split in half lengthwise.
The home cook can achieve this cut a variety of ways. If you don't have a green bean Frencher, carefully run a paring knife between the seams of the bean so the seeds end up exposed and facing outward.
Another way that's a bit of a shortcut and finger-saver for those with less-than-stellar knife skills, is to slice the green bean at a 45-degree angle into thin ribbons. Perhaps not a true "French cut," it still achieves a similar effect.