Tree fruits aren't necessarily harvested in the same way that normal plants are. You get apples/coconuts from Apple Trees and Palm Trees by either waiting for them to drop the items or cutting them down. Keeping in mind that they only produce these items in the correct season (generally summer).
So, with all that in play, you should be 'harvesting' apples and coconuts as long as your forester is cutting down those trees in Summer. Which they will automatically do if you have the arboretum set up around those trees.