Dan Quayle has certainly uttered his share of malapropisms, solecisms, and straight-up absurdities, but he didn't say this one. According to the indispensable urban-legend-debunking website Snopes.com, the quote originated in 1989 with Representative Claudine Schneider of Rhode Island, a Republican.
Speaking to a group of fellow Republicans, she recounted that the she and Quayle had attended an event at the Belgian embassy, where then-Vice President Quayle complimented Representative Schneider on her command of French (this was back when speaking French wasn't regarded as a political liability).
Schneider then attributed to Quayle the belief that Latin was the lingua franca of Latin America, before concluding that the whole story was a joke. But many publications, including Newsday, The Chicago Tribune, Newsweek, and Time, reported Schneider's joke as fact, further cementing in the public consciousness the perception of the vice president as an intellectual lightweight.
