Florence gas optimizations are only about the Michelson interpreter.
During a call to a smart contract, gas is charged for the following things:
checking the signature of the operation
account management (debiting the caller and crediting the smart contract)
fetching the script and the storage of the contract from disk
conversion from a byte sequence to an ...
As commented above, https://tezos.gitlab.io/introduction/test_networks.html lists the current networks: mainnet, Edo2Net (mainnet test), Florencenet (next protocol, if it passes)
Every network is public and both test networks have free tokens from the faucet. You can participate by downloading/running the latest tezos software and using the --network flag to ...