The singer joins more than 17,000 people who have signed a petition calling on Stafford Borough Council to reject the planning application.
Protesters say the facility, which would be built in Radmore Lane, Gnosall, near Newport, is unethical and would keep rabbits in tiny cages.
The planning application, which has been submitted to the borough council for consideration, is to build an intensive rabbit farm.
The singer signed the petition endorsing a letter from the People for the Ethical Treatment of Animals (PETA) Foundation. PETA believes the rabbits would be condemned to lives of misery.
Campaigners warn the proposed farm could also pave the way for fur farming to sneak in through the back door. They claim it appears the farm would "derive a substantial part of its profits from selling rabbits' skins".
But Romanian food wholesaler POE Limited, which has lodged the application, said the plan is only in the early stages and it would consider the welfare of animals should it be given the go-ahead.
PETA director Mimi Bekhechi said: "PETA, Fran Healy and thousands of concerned citizens are urging the council to see the light – something rabbits on factory farms seldom get to do – and reject this application.
"Rabbits raised on factory farms rarely, if ever, smell fresh air or feel the warmth of the sun on their backs before they're sent off to slaughter."
According to PETA, the cages rabbits would be kept in are about 70cm long and 40cm high.
Protesteors say the rabbits would be unable to stretch out, rear on their hind legs, hop, dig or carry out other natural behaviour. They also fear rabbits would be kept in "individual barren cages without any enrichment or bedding".
Speaking after the application was lodged, Alina Muntean, of POE Limited, said: "First of all we haven't done anything yet. It's just planning permission for which we have applied for. So nothing has been built yet.
"I received an email from the animal rights group with this concern regarding animal welfare, but as of yet we haven't considered what the animals will be doing, whether they'll be free and jumping around or anything. I have nothing to say in this phase because nothing is there yet."