The French dish that is a thick, chilled soup of leeks and potatoes is vichyssoise.
Vichyssoise is made by cooking and puréeing leeks, potatoes, onions, and cream, then serving the smooth soup cold. Chopped chives are a traditional garnish. Its creamy texture comes from the puréed potatoes and dairy rather than from a roux or other thickener.
The soup was created in the early 20th century by Louis Félix Diat, a French-born chef who worked at the Ritz-Carlton Hotel in New York. Diat said he was inspired by the leek-and-potato soup he remembered from his childhood near Vichy, France. The dish’s name refers to Vichy, although its documented modern creation took place in the United States.
Vichyssoise is related to older French preparations called potage Parmentier or potage à la Parmentier, which were hot leek-and-potato soups. That relationship explains why the soup can seem more traditionally French than its origin story suggests. Bouillabaisse is also French, but it is a hot seafood stew associated with Marseille, not a chilled vegetable soup.