Buy a replacement plug. Put a #10 between the neutral terminal and the grounding terminal. System is bonded while that is installed. If all you have are GFCI receptacles on the generator, this bonding plug may pop the GFCI's and is not really in the right place, so you need to use a non-GFCI receptacle or find an internal point in the wiring compartment to do this bonding.
GFCI's will aid safety of a generator, grounded or not. But if it isn't grounded, it would be rare to get a leakage path or shock that will trip a GFCI. If the generator frame made a good enough ground electrode and you have a N-G bond, then perhaps GFCI's would help. Nothing is going to save you if you get between the neutral and hot of the same branch circuit.