In France, more often than not, you will be served little pale-green flageolet beans with lamb. I don't know where that tradition came from. A gigot is a leg of lamb, and the Larousse Gastronomique food and cooking encyclopedia says: Le gigot rôti, piqué d'ail et accompagné de flageolets, est le plat traditionnel des fêtes familiales et des repas fins. The Grand Robert dictionary says that the flageolet bean is « très estimé » — "highly prized."
What are flageolet beans anyway? The LG says they are small, green or white beans that are grown in Brittany and in the north of France. They are harvested slightly immature, in August and September, and you can find them dried, canned, or frozen in the supermarkets. I remember reading somewhere that flageolets, also called chevriers, are closely related to the French haricot vert green bean, or maybe even the same plant.
The LG also says that in the Touraine region, where we live, dishes prepared « à la tourangelle » are large cuts of mutton or lamb that are roasted, served with their natural juices, and accompanied by « une garniture de haricots verts et de flageolets liés à la béchamel claire ou au velouté. » You often see flageolet beans and green beans cooked and served together.
By the way, a flageolet is also a little flute. I think the name for the beans is an allusion to the fact that they make you toot after you eat them. We had our flageolets and some Tuscan kale as the garniture (vegetables) that we ate alongside our rolled-and-tied, boneless leg of lamb yesterday.