F-Droid is an installable catalogue of FOSS (Free and Open Source Software) applications for the Android platform. The client makes it easy to browse, install, and keep track of updates on your device.
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Most phones that have an FM Radio chip installed have a radio app pre-installed that works just fine. If you don't like that one you can try iHeart Radio.
If your phone doesn't have an FM Radio Chip, you won't be able to listen to radio without internet.
The radio app that came with your phone, perhaps?
Those apps need to be system installed, so if your phone/ROM didn't come with one other user installed apps won't probably work.
Also cord headphones are used as antenna, if if your phone don't have a headphone jack there's no way to make it work
A radio perhaps