The imposition of costly tariffs could price local lamb producers out of the French market.
That would be very costly for the industry here, which exports a large amount of produce there.
The Ulster Farmers’ Union beef and sheep chairman Sam Chesney said that a loss of access to French consumers would be “devastating”.
France currently takes around half of UK sheep exports.
Mr Chesney said the loss of the market would mean large numbers of farmers turning away from sheep meat production.
About 80% of the 25,000 farms in Northern Ireland are beef and sheep businesses.
“There would probably be very few sheep left in Northern Ireland, it’s as bad as that,” he said.
He said if sheep farming reduced it would have an impact on the environment in upland areas.
“The hills and the Glens of Antrim are shaped by the livestock on them. If they weren’t there, the hills would go to rack and ruin, it would be land abandonment really.”
EU tariffs under a no-deal scenario would make UK lamb products half as expensive again for customers.
Beef products would face a tariff of around 80%.
The Ulster Farmers’ Union and the operators of Northern Ireland’s meat plants have joined forces to call for a trade agreement that would ensure a no-deal scenario is avoided.