Actually you can build a simple FM receiver with the same parts you would use for a simple AM receiver, if you are willing to accept a fair amount of distortion. It would not be great for music, but would be OK for receiving news or weather or emergency instructions.

One way to do this is to use something called an "FM slope detector" [1]. The idea is that you have a tuned circuit tuned to slightly above or below the carrier frequency of the FM signal. As the FM signal frequency moves around, it also moves nearer and farther from the center frequency of the tuned circuit, which means the output of the tuned circuit rises and falls. The result is that the frequency modulation of the FM signal gets turned into amplitude modulation of the output of the tuned circuit.

You can demonstrate this if you have one of those cheap SDR dongles. Tell your SDR software to decode as AM, but tune to an FM broadcast station, and then start slowly moving the tuning up, and you'll find a point where the broadcast becomes quite intelligible.

[1] https://www.electronics-notes.com/articles/radio/modulation/...