French regional cuisines use locally grown vegetables, such as: 1  Potatoes. 2  haricot verts (A type of French green bean). 3  Carrots. 4  leeks. 5  Turnips. 6  Aubergine (eggplant). 7  Courgette (zucchini). 8  Mushrooms, oyster mushrooms, cepes (cèpes). 9  Porcini. 10  Truffle.  shallots