The winger is keen to secure a return to the national team ahead of next year's World Cup in Brazil.
Ben Arfa was involved in an altercation with Blanc during last year's European championships, after he was told not to use his phone at half-time when Sweden were winning 2-0 in the group game.
Since then, Blanc has been replaced by Didier Deschamps, a manager the midfielder played under at Marseille - but the Newcastle man's international career remains uncertain.
Ben Arfa told France Football magazine: "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. It's not correct. I regret this behaviour. I want to apologise to him."
The 26-year-old is targeting consistency with the Tyneside club and believes club form is key to realising his international ambitions: "I know I can bring something to this France team. 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."
Ben Arfa, who has 13 caps for France, also faces the task of clearing the air with Deschamps, who was less than impressed with the manner in which the attacker forced through a move to Newcastle back in 2010.
"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.
"With Deschamps, it's different. I would rather explain myself to clear the air."
The Clairefontaine academy graduate has enjoyed a successful start to the Premier League season with two goals, and a number of impressive displays for Newcastle.
Should Ben Arfa be given another opportunity on the international stage?