I've been reading several books lately about the way the French eat. It's been pretty enlightening, really. Their super power lies in portion control. That way they still get to drink wine with meals. ;)
Provençal refers to anything related to Provence. It is the birthplace of salade Nicoise, a salad that contains as one of its ingredients something called haricots verts. That translates to green beans, but they are skinnier, and more expensive than what most of think of as green beans. So this recipe uses regular green beans. If you wanted to make it more "French", you could hunt down some haricots verts.
French Style Green Beans
One pound green beans, ends snipped and then cut into 1 inch pieces
One can of diced tomatoes
One onion, chopped fine
Two cloves garlic, minced
Salt and pepper
Saute the onion and garlic in oil until softened. Add them, plus the oil, to a crock pot. Add the green beans and tomatoes to the crock pot, and season with salt and pepper. Stir well, cover, and cook on low for about six hours. Serve. Enjoy!