All 149 passengers were forced to disembark as the plane was impounded at Bordeaux-Merignac airport on Thursday as a "last resort".
The airline has now entered negotiations with the department over how to repay more than €500,000 at the centre of the dispute, regional newspaper Charente Libre reports.
"It is unfortunate that the state had to take such action, which led to the inevitable inconvenience of the 149 passengers on board", the aviation authority said.
The authority did not specify the amount owed by Ryanair.
Ryanair had been ordered for some time to pay back funds that the European Union had declared to be illegal subsidies.
An appeal against the judgement was rejected by the tribunal administratif in the summer.
Ryanair was reportedly paid French subsidies that were later deemed to be illegal.
'Just because we manage a little airport in Charente it doesn't mean we are not going to defend ourselves'.
Storms, strikes, computer failures - you can now add "your plane has been seized by the government" to the list of things that can delay your flight.
The move on the plane, a Boeing 737, on Thursday at Bordeaux's Merignac airport in southwestern France came after Ryanair failed to respond to a final warning delivered in May, prompting the order to seize the aircraft, DGAC told AFP.
The EU also ordered authorities to recoup money from Transavia over benefits they had received at two other French regional airports.
The pan-European stoppages prompted the airline to cut its profit forecast, but it still expects to make profits after tax of 1.10-1.20 billion euros in its current financial year.
HuffPost UK has contacted Ryanair for comment.