Digital FM Demodulation
Assuming you understand how the FM signal is theoretically generated, here is a simplified strategy to start with. In an FM Signal (https://en.wikipedia.org/wiki/Frequency_modulation), the frequency of the carrier is modulated according to the message signal (mostly audio). The instantaneous frequency $f_c(t)$

$ f_c(t) = k*m(t) + f_0$

where $k$ is a modulation constant. The phase of the carrier as a function of time is

$\phi(t) = \int f_c(t) = k t m(t) + f_0 t + \phi_0$.

Theoretically you FM signal have infinite BW but as per the Carson's rule most of the BW is concentrated around $f_c$. You have to make sure that the IQ samples had sufficient BW around $f_c$. 
Once you extract the phase information from IQ samples, you can take first differential $\phi_n - \phi_{n-1}$ to get the instantaneous frequency information $f[n]$. The message signal $m[n]$ will be a proportionate of $f[n]$. With the knowledge of $k$ you should be able to get back (demodulate) the message signal. There are a lot of assumptions here though. You should be aware of $k$, Bandwidth of message signal, $f_c$ the center frequency etc.