There are several foods that you can take for a picnic that are not messy and easy to carry. For example potato salad, fried chicken, water melon, pasta salad, sandwiches, bread, cheese and many more. These will make the picnic fun and not mess your picnic basket.
What ever you decide, be sure to observe proper food safety so no one ends up sick. For instance, if you take potato salad or uncooked meat be sure it remains chilled, as these items can turn bad quickly.