Okay i tried, but this is in no way a viable circuit. In reality making it will fail miserably.
How it works: I'm not going to get into the modulator part. It's just a VCO 555 timer well above its maximum operating frequency. The Demodulation works something like this. First you apply the modulated signal through a specifically chosen LC filter with a given Q factor. As the FM deviates in and out of the LC filter's center frequency the frequency shift gets converted into an amplitude shift. This means that the FM must first be converted to AM before any further demodulation. Then it's a simple matter of envelope detection (the diode and everything to the right of it). Here's a youtube link of an army training film that explains it in detail. https://youtu.be/xn6lzrMJUDs and another one https://youtu.be/gfz1FbIOMbs