I have used a similar construction method and have never seen any issues with static build up. It was just for thermal storage in a residential home. Like Carl mentioned in the comments the rug and pad would either isolate it or conduct to the surroundings. However, if this design is to be used in an electronics or pyrotechnics manufacturing facility you will indeed want to take some extra precautions.
To ground the internal floor to the foundation I would recommend running 6 gauge copper wire (mainly for flexibility and durability) from a ground clamp on rebar in the foundation to a ground clamp on the floating floor structural remesh. The structural remesh will be sufficient. That will certainly address any static issues, but it is always a good idea to check the NEC (NFPA 70) and your local electrical codes before a construction project. Even if grounding was not required by code, they may require any grounding you add to be installed by an electrician (if not your personal home).
Another option is to install a dedicated ground rod or rods in or below the floating floor. Might be easier than messing with connections to the foundation.
If this is for a static sensitive application you will need to consult with a company that specializes in this. They will help specify conductive flooring, facility grounding, low static generating materials, HVAC systems and controls, garment specifications, etc.