The Newcastle United forward reacted angrily after Blanc told him he could not use his phone at halftime in the dressing room after their 2-0 group stage defeat against Sweden last year.
"It is true that I messed it up. I had come out of this game very frustrated. I was only thinking about myself. And when Laurent Blanc made his remark about this phone call I received in the dressing room, instead of shutting my mouth, I talked back. I should not have," Ben Arfa told France Football magazine.
"It's not correct. I regret this behaviour. I want to apologise to him."
Ben Arfa, who was ruled out for almost a year after a leg fracture in Oct. 2010 just after joining Newcastle from Olympique Marseille after refusing to play for OM, also admitted he had not been well behaved with his then Marseille coach Deschamps.
Deschamps has overlooked Ben Arfa since taking charge of the national side after the Euro 2012 finals. Les Bleus have secured a World Cup playoff spot and are hoping to feature in next year's finals in Brazil.
"We have crossed paths once since (the Marseille incident). We greeted each other, but it is true that our previous conversation had been a heated one," Ben Arfa said.
Asked whether he also wanted to apologise to Deschamps, Ben Arfa replied: "Yes, obviously. But it's not the same apologies than with Laurent Blanc. With Deschamps, it's different. I would rather explain myself to clear the air."
The 26-year-old Ben Arfa, who won 13 caps for France, scoring two goals, has been in fine form for Newcastle this season and has been tipped to shine for France by his club manager Alan Pardew.
"I know I can bring something to this France team," he added.
"But before claiming anything I need to be consistent at a high level with my club. If it works out well, I can't see why I would not go back to Les Bleus."