I guess this may clear your dobt. I don't think so because "sondern" means "but rather" which means you want to show a contradiction or a comparison of the same category or a specific group. Eg: Sie trinkt nicht Orangensaft sondern Apfelsaft.(Comparison between fruits) She does not drink orange juice but rather apple juice. However,if we use außer which means except it won't make sense.
Why not: "He eats nothing, excepting fruit." https://en.oxforddictionaries.com/definition/excepting
The reason for Duolingo having included this sentence is to show us that Obst is taking the dative case here, right? It's kind of hard to notice since it doesn't actually have an article.