That's not going to work. If you are originating your first flight at ORD, the award structure would have to be:
Award 1: ORD-HNL
Award 2: HNL-ORD(stop)-MXP
Award 3: CDG-ORD
Where you COULD save awards is if you were doing a Hawaii vacations every winter and European vacation in summer. Then you could do (as an example):
Award 1: ORD-HNL
Award 2: HNL-ORD(stop)-MXP
Award 3: CDG-ORD(stop)-HNL
Award 4: HNL-ORD(stop)-MAD
Award 5: MAD-ORD(stop)-HNL
And so on...
The thing is that first flight has to be handled separately. You can start using the free stopover on the SECOND flight.