You ask a very important question that I must admit I do not know the full answer to. However, the roots of the perceived 'superiority' of French cuisine date back to at least the French Revolution. According to Rebecca L Spang, The Invention of the Restaurant: Paris and Modern Gastronomic Culture (Cambridge, Mass.: Harvard University Press, 2000), food criticism as a genre of writing, and gastronomy as a field of expertise, originated in France under Napoleon III. Generally the first recognized professional 'food critic' is Grimod de la Reyniere with his Almanach des gourmands [online here--and well worth reading!!!] Spang writes:

"Gastronomy exempted itself from incendiary questions of subsistence, and placed the table squarely in the realm of literary or artistic debate."

All that being said, there's definitely an involved and complicated story that I am not expert in about the American relationship to French cuisine during the twentieth century. As recently as the 1920s, even tomatoes, basil, onion, and garlic, were seen as 'dirty,' foreign cuisine, unlike good ol' all-American meat, potatoes, and a green vegetable on the side! (The midwestern diet became universalized as the 'American diet' especially in the military canteens of World War I where Americans from all regions fed on the same food.) The disgust people felt for garlic rivaled the way the average American now reacts to hearing that some cuisines include dog or horse meat. [Harvey A Levenstein, Paradox of Plenty: A Social History of Eating in Modern America (New York: Oxford University Press, 1993).] I must admit, however, that I do not know whether or not French cuisine received the same scorn that Italian cuisine, Eastern European cuisine, and even Scots-Irish cuisine did and still often does! (How often have you heard haggis used as an example of utterly gross food-stuffs? -- it is the American immigrant communities' versions of these cuisines that we now embrace)

However, French cuisine undoubtedly experienced a huge boost in prestige thanks in no small part to Julia Child and her famous "Mastering the Art of French Cooking" first published in 1961. Not coincidentally, she is often credited with inaugurating the practice of having a glass of wine with dinner. After her came the rise of even counter-cultural 'high cuisine' that relied on french roots for its prestige - see Alice Waters and her revolutionary restaurant Chez Panisse, founded in 1971 in Berkeley California, famed for local whole foods cooking. [Warren James Belasco, Appetite for Change: How the Counterculture Took On the Food Industry, 2 edition (Ithaca: Cornell University Press, 2006). ; Laura Shapiro, Something from the Oven : Reinventing Dinner in 1950s America (New York: Viking, 2004).]

A huge shift came with what as know as "The Judgement of Paris" - a 1976 blind wine tasting competition/event in Paris. In this blind tasting, the world expert judges acclaimed California Chardonnays and Cabernet Sauvignons to be better than the French counterparts. This absolutely ROCKED the culinary as well as wine-loving world--literally the equivalent of the Miracle on Ice (where the rookie US hockey team somehow beat the Russians in the 1980s Olympics). Since then, the pendulum has been swinging wildly; French cuisine still has centuries worth of residual prestige but American and fusion cuisines now rival classical French easily. [accumulated knowledge]

EDIT: Inserted the wrong quote the first time, which was going on about the political valences of eating in the era of the french revolution! Correct quote now.