Under the Florida residential landlord tenant act is a lease agreement still valid of landlord's agent signed the lease?

Possibly. It depends on whether the agent had authority to sign on the landlords behalf. Often the landlord signs an authorization and that is all the agent needs. Your copy of the lease may have just the typed name but if the landlord has the original, they will probably sign it before any legal action is started.

If there is no valid lease, then you are probably on a month-to-month tenancy (assuming you pay rent on a monthly basis) and you can terminate the lease agreement without finding a new tenant. For a month-to-month tenancy, you have to provide fifteen days notice of intent to terminate the lease.