Dry white wine is the best option to use for a French onion soup recipe. Most people like a selection of wine that is not too sweet or fruity for this particular soup. Red wine would be great as an ingredient when making a seafood dish.
It's really a natter of taste. Personally for French onion soup I'd use dry, as I would expect the sweetness might interfere with the onion flavor. The general rule of thumb is, don't cook with a wine you wouldn't drink.