The final choice to make "A Moveable Feast" the title was made by Hemingway's fourth wife, Mary. It was supposedly suggested by Hemingway's friend, A. E. Hostner.
While the Hemingway quote is certainly the source of the title, the phrase "A Moveable Feast" clearly predates Hemingway. It originally referred to a Roman Catholic feast not associated with a specific day of the year. If we look at the phrase in a secular context, it can be interpreted as a celebration that can happen at any time. We can see this characterization fall into place when we consider the French title of the book, Paris est une fête ("Paris is a party").
Hemingway's life in A Moveable Feast is, of course, quite the party. Consider first the company he keeps. Visits to the always entertaining Gertrude Stein (along with her partner Alice Toklas) become a common staple and a source of news from and of other American expatriates. Dinners and other social events with F. Scott Fitzgerald and his wife Zelda also played an important part. The Fitzgeralds, if I remember correctly, were not ones to refuse a drink, and Hemingway was influenced by them. Their travels to Spain and coastal France led to further trips there for Hemingway, leading to his famous novel The Sun Also Rises.
Another important element of the book is the classic Parisian café. Cafés could were sanctuaries for Hemingway, sources of company as well as sources of solitude and places to write. I'd suggest that it is not food that connects the cafés to the title, but rather simply the luxury of being able to sit, drink, and write at one's pleasure. Hemingway's leisurely walks through the streets once in a while - often ending at a café or bookstore - also allowed him time to think.
I do agree that the idea of an eternal Paris - perhaps even an eternal Parisian spring - is expressed quite nicely by the quote. Recall the title of the last chapter: "There is Never Any End to Paris". Set as the Hemingway family vacations in the Alps, it marks the end of Hemingway's celebratory time in Paris as one of the young writers of the Lost Generation. He has matured, both as a man and as a writer (He then dates Pauline Pfeiffer, which leads to the end of his first marriage, and a different kind of end to the period). The chapter also marks the beginning of the end of the Roaring Twenties as a whole, leading up to the worldwide Great Depression.