whoBIRD

An app that recognizes birds singing near you, all on device, and has an option to show a photo of the bird too. It's exclusive to F-Droid (not on Google Play), and the only bird recognizing app I know of that does it all immediately on your device (without sending it to a server). https://f-droid.org/en/packages/org.woheller69.whobird/

Organic Maps

Highly detailed OpenStreetMap maps local on your device. Wonderful for walking directions, as it has on-device routing and maps out walking pathways (which is something that even Google Maps does not do well) https://f-droid.org/en/packages/app.organicmaps/

AntennaPod

The best podcast client also happens to be Free Software and on F-Droid. https://f-droid.org/en/packages/de.danoeh.antennapod/

HeliBoard

This is the best FOSS keyboard that's under active maintenance. It even supports swiping, but that requires a non-free binary library from Google. (Maintained fork of OpenBoard.) https://f-droid.org/en/packages/helium314.keyboard/

Breezy Weather

Good weather app that has so many details (including pollen too) and fetches from multiple sources. It looks great as well. https://f-droid.org/en/packages/org.breezyweather/