If you are sensitive to fructose, you don't have to eliminate all fruits, but only fruits that contain more than half of their natural sugars as fructose. The high-fructose fruits you should avoid include apples, cherries, mangoes, watermelon and pears.You can safely have moderate amounts of low-fructose fruits, such as honeydew melon, cantaloupe, bananas, blueberries, strawberries and oranges, if they are well spaced throughout the day.void sweeteners that are rich in fructose, especially honey, high-fructose corn syrup and agave syrup. If you want to add a sweet touch to your diet, use lower-fructose alternatives, such as maple syrup, brown sugar, granulated sugar, stevia or artificial sweeteners, to keep your intestines happy.