I looked these up on Wikipedia so take them for what they are worth. The second term I am not sure about.
Mille-feuille (French: thousand-layers) is a type of pastry consisting of two thin sheets of pastry, many layers of filo pastry, or puff pastry laid on top of each other much like a sandwich with either sweet fillings like jam, crème patissière, and/or whipped cream spread on the inside with a thin layer of icing (usually lemon icing) on top dusted with powdered sugar, or savory fillings like cheese.
Haute cuisine (literally "high cooking" in French) or grande cuisine refers to the cooking of the grand restaurants and hotels of the western world. It is characterized by elaborate preparations and presentations; large meals of small, often quite rich courses; extensive wine cellars; and large, hierarchical and efficiently run service staffs. The cuisine was defined by the French cuisine classique until the 1970s, when cuisine classique was supplanted by nouvelle cuisine. Nowadays, haute cusine is not defined by any particular style – there are haute cuisine restaurants serving fusion cuisine, regional cuisine and postmodern cuisine – but rather by careful preparations, elaborate service, obsessive attention to detail, and, most importantly, critical acclaim. Culinary guides such as the Michelin Guide and Gault Millau have helped to define modern haute cuisine, although some have suggested that their influence is on the wane.
Nouvelle cuisine (French for "new cuisine") is an approach to cooking and food presentation. This new style, which was a reaction to the French cuisine classique, called for lighter, more delicate dishes, without heavy sauces and overcooked vegetables, and placed a higher importance on presentation. The style called for simplicity and elegance in creating dishes. It was developed in France in the 1970s by students of Fernand Point, particularly the brothers Jean and Pierre Troisgros, Paul Bocuse and Michel Guerard. The term was coined by the food critics Henri Gault and Christian Milleau. Nouvelle cuisine became popular in the late 1970s and 1980s.
Food presentation and visual appeal are paramount in nouvelle cuisine. The food had to excite all five senses, especially the visual. The reliance on the wait staff to present the food, as is the norm in haute cuisine, was abandoned. Courses were served already plated. Herbs and spices were used extensively, and sauces and stocks were much lighter. Flour was rejected as a thickener in favour of presenting thinner sauces thickened with egg yolks, butter and cream. Nouvelle cuisine created light dishes with distinct tastes – combining flavours instead of overruling them – and emphasised less intrusive service. Elegant yet simple dishes and pure tastes are the hallmarks of nouvelle cuisine.
There is a standing debate as to whether nouvelle cuisine has been abandoned. Much of what it stood for – particularly its preference for fresh flavours lightly presented – has been assimilated into mainstream restaurant cooking. While Nouvelle Cuisine's emphasis on small portions (and large plates) has often made it an object of ridicule in popular culture, its influence in haute cuisine and even in more quotidian restaurants is widely felt.
While nouvelle cuisine was once considered a radical departure from the cuisine classique, which was strictly based on the canon of Auguste Escoffier and Antoine Carême, it no longer has the same sense of radicalism. It has been supplanted, in this respect, by the postmodern cuisine or molecular gastronomy of such chefs as Ferran Adrià, Heston Blumenthal and Homaro Cantu.