Most fast food establishments offer a depressingly limited wine list. You may have to supplement by bringing your own bottle inside the McDonald's. If you do so, make sure that you're choosing the right wine. Dominique Zamora has some good suggestions, such as this Clara Brut champagne which has a honey tone that accompanies Chicken McNuggets well.
You can read her other wine pairings at the link, including selections for Taco Bell, Kentucky Fried Chicken, Subway and other gourmet eateries.