My question is whether there are some predefined python bindings to control the mocap manager from remote (I would just need to start the recording, and eventually set some string, like session name, …).
I have already used the same approach with take recorders, which exposes a few python bindings.
In case the answer is no,
Does someone know how to expose those functions in python, using c++?
Thank you community,
you are the best 
There are no pre-defined python bindings for mocap manager since it is almost entirely constructed from Editor Utilities.
If you want to start and stop recording you can make calls to the take recorder sub system, which is available from python. Mocap manager respects these calls.
To create a new session you could get the PCap Viewmodel and call the create new session method directly. You should be able get the Pcap Viewmodel from it’s view collection, which is owned by the PerformanceCaptureSubsystem.