The captain said he decided to divert to the central French city of Limoges as he felt the incident was endangering the other passengers on board.
Both men were taken to a local police station. The men were initially referred to as Liverpool football fans in a initial report by AFP, but a later version withdrew any reference to football fans.
Passenger John McMullen told the Local that the men were part of a stag party rather than football fans.
“They are being held while they sober up, and between them being drunk and the language barrier, it is difficult to be certain about their reasons for the fight and going to Spain,” said a police spokesman.
“The two men will be heard later in the day, when an English-speaking interpreter is present.”
The Boeing 737, carrying just over 180 passengers, was able to resume its flight to Spain.
A statement from Ryanair sent to The Local read: “This flight from Liverpool to Alicante (28 Apr) diverted to Limoges after two passengers became disruptive in-flight. The aircraft landed normally and police removed and detained these passengers before the aircraft departed to Alicante.
“We will not tolerate unruly or disruptive behaviour at any time and we sincerely apologised to other customers for any inconvenience caused. The safety and comfort of our customers, crew and aircraft is our number one priority.”