The Rehabilitation Center at Hollywood Hills filed the lawsuit September 19 and followed with the amended complaint Tuesday, contending that the state did not have adequate grounds to prevent the facility from operating.
Franco's husband, 93-year-old Miguel Franco, also died after the tragedy.
Franco lived only 26 days after her husband of 61 years, Miguel Antonio Franco, died along with seven other residents in the first run of deaths.
The state has suspended the home's license.
Cecilia Franco, 90, died on Monday, the 13th person from the Hollywood nursing home to die following a power outage caused by the hurricane.
Four more people later died, and the Hollywood Police Department has launched a criminal investigation into the deaths.
Cecilia Franco would be the 13th death linked to the nursing home.
Ninety-year-old Cecilia Franco died early Monday morning, almost a month after Rehabilitation Center at Hollywood Hills' air conditioning broke for several days, and the care facility did not evacuate patients.
When the hurricane hit South Florida on September 10, one of the nursing home's transformers powering its cooling system went down.
Last week, it was announced that the facility had laid off 245 workers.
Nursing home residents were exposed to the heat after Hurricane Irma downed a tree that knocked out the transformer powering the air conditioning system.
"This facility is failing to take responsibility for the fact that they delayed calling 911 and made the decision not to evacuate their patients to one of the largest hospitals in Florida, which is directly across the street", Scott said in a statement last month.