Not being Airbus, but IDG's are usually connected and driven by the HP (N2) system (N3 on some RR types) and the guarded flight deck switch will physically cause a solenoid to bring about a drive disconnect; re-connection is only possible when the engine is static on the ground.
When the IDG looses drive or under-speeds, the associated generator control unit, GCU, will take it off line by de-exciting it and opening its GLC.
On the B727 there was a field control switch/contactor, but the FE could also adjust the frequency and parallel generators, that is old techy.