The free sharing contract says you can't keep pets, but how can you sue if you do?

Bring a civil lawsuit. Bring a lawsuit to the court with the shared lease contract, demanding compensation for the loss without compensation. If you violate the terms of the lease contract at will, it will affect the legitimate rights and interests of Party B, so you can consider bringing a lawsuit to the court to investigate the legal responsibilities that Party B has not undertaken in accordance with the terms of the contract.