If the type of modulation you are talking about is FM, then the spectral content depends on its modulation index (M or $\beta$).  The full equation for the output is (for a sinusoidal input only):

![FM modulation with tones][1]

The term inside the cosine is not easy to isolate.

With some algebra it can be separated out using bessel functions:

![enter image description here][2]
![enter image description here][3]
![enter image description here][4]

So you can see that this signal has frequency components at $f_c + n*f_m$.  Where n is $-\infty$ to $+\infty$.  **Shocking isn't it?**  The Bessel Function $J_n\{\beta\}$ tends to approach zero at large values of n, but it is counter-intuitive to see all this frequency content.

So a simple sine wave modulation at frequency Fm can produce a variety of spectra depending on its modulation index (M or $\beta$) which is a ratio of the change in frequency deviation ($\Delta$f) to the maximum frequency of the modulated signal ($f_{m(max)}$).  See the plots for different values of M for the same modulating tone at frequency $f_m$ where $M=\frac{\Delta f}{f_m}$

![FM spectra][5]

In reality, [Carson's Rule][6] is applied to limit the spectral content to about 98% of all the energy.  This bandwidth is double the frequency deviation plus the maximum frequency of the input modulation content.

![equation][7]

So to answer your question the spectral content is not necessarily directly related to the modulated signal spectra with FM.  It's periodic, sure, but there is a lot of content.  If you knew the exact modulation parameters you could try to work backwards and estimate the modulated input based on relative amplitudes and spectral frequencies.

  [1]: http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/RadCom/part12/Images/page1/Eqn31.gif
  [2]: https://i.sstatic.net/k6gS3.gif
  [3]: https://i.sstatic.net/wLNy2.gif
  [4]: https://i.sstatic.net/lTNZa.gif
  [5]: https://i.sstatic.net/hACMV.gif
  [6]: http://en.wikipedia.org/wiki/Carson_bandwidth_rule
  [7]: https://i.sstatic.net/sRA7V.png