First of all, let's get a few things straight.
- The FCC has a partial agreement for space launches, specifically, they are allowed to regulate the use of frequencies, etc.
- The FAA is allowed to regulate the spacecraft, launch site, and the timing of the launch, and similar such things. But their power pretty much stops at the atmosphere.
In essence, as virtually every satellite has to talk to someone at some point in time. As a result, the FCC is allowed to regulate satellites and other similar machines pretty well. They have done so, by doing things like ensuring that the spacecraft can de-orbit prior to allowing it an FCC license, for instance.
As far as inter-government organizations, there are quite a few that regulate how things work. The main one is the International Telecommunication Union, which is the equivalent to the FCC from the United Nations. Specifically, they have a Space Services Department, which
The Department handles capture, processing and publication of data and
carries out examination of frequency assignment notices submitted by
administrations for inclusion in the formal coordination procedures or
recording in the Master International Frequency Register (MIFR).