If you want individual trees, it's difficult/useless to do because

1. natural=tree is not commonly used in general (~30000000 usages out of an estimated ~3000000000000 trees)
2. There's no tagging specifically for "fruit trees"
3. There's a much more detailed tag for the species of an individual tree (genus, species/species:wikidata, taxon) but they are rarely used (only ~4M usages total out of ~30M trees mapped)
4. You would have to list the species you would classify as "fruit trees", which are probably a lot of species, and then also do a search for all 4 of the tags listed above. As it's quite a complicated thing, you would probably need a more advanced tool for searching, like Overpass. Here are all the apple trees in a random bit of Italy: https://overpass-turbo.eu/s/269o . There are obviously a lot more apple trees in that bit of Italy than the literally one that's mapped currently. As I've said the trees are not well-mapped (yet).

If you're looking for groups of fruit trees planted by humans, that's landuse=orchard, and while there are only ~1.6M uses of that, it groups a lot of trees together so might be more useful for you. You can search for orchards in OsmAnd (which is way more versatile anyway, if your hardware can run it I definitely recommend it over OrganicMaps) - just type in "Orchard" into the search bar.

If you're looking for orchards of a specific tree, there's the trees by which you can filter. But you'll once again need Overpass. For example, here are all the mapped apple orchards in the same random bit of Italy: https://overpass-turbo.eu/s/269q (once again, there are probably way more but most are not mapped yet).

N.B: I've just realised that monospace links are not well-highlighted on Lemmy, so FYI all the tags/keys above are links that you can click to learn more