The two sides will meet in Lyon on Sunday for the first time since the night in November 2009 when the Frenchman broke Irish hearts by helping to deny them a trip to the World Cup finals in South Africa in controversial fashion.
Memories of that game have inevitably been rekindled since the Republic booked their place in the last 16 with a 1-0 victory over Italy in Lille on Wednesday evening, but manager O'Neill believes it is more of an issue for Henry's compatriots than it is for his players.
The 64-year-old said: "The Thierry Henry [incident] is still probably causing some controversy - maybe more in France than it is in Ireland.
"I think we have decided to forget about it - that's something coming from Ireland. It will be a talking point obviously, but I don't think it will concern us when we play the game."
O'Neill is the first Ireland manager to lead a team into the knockout stages of a European Championships, although he did enjoy a World Cup adventure as a player with Northern Ireland back in 1982.
They defeated host nation Spain on their way to the quarter-finals and having seen off the Italians, the Republic boss is hoping for a repeat 34 years on.
He said: "When I think about it there are definite similarities. We went on a journey in 1982 that brought us up against the host nation, who we had to beat to get through to the quarter-finals, and that was an immense moment for us and one that I will never forget.
"There are similarities between that and now facing France on Sunday. It's a game that we will look forward to - we must look forward to the game, but not just look forward to it, actually believe that you can compete and win the game.
"We have to think that because the performance last night will give us an enormous boost of confidence and we need to carry that through."
However, it is the present which most concerns O'Neill as he faces a quick turn-around after a dramatic night in Lille with full-back Stephen Ward a fresh injury concern after damaging an ankle against Italy.
France finished their Group A fixtures on Sunday, giving them an extra three days' rest, although the Ireland manager is not too concerned by that.
He said with a smile: "It does seem a disproportionate amount of time that one team has to recover from another. That might become very important.
"I understand that, as the host nation, you should get some favours. If the competition was in Ireland, I would do exactly the same myself. Teams that play Ireland would play every single night and we wouldn't have to play for a year."
O'Neill and his players did not get to bed until around 5.30am on Thursday after travelling back to their base in Versailles, although spirits were understandably high after a memorable night.
The former Celtic boss said: "The evening last night was reminiscent of some great European nights at Celtic.
"We had a great European night against Juventus some years ago, the place was absolutely rocking. We followed that up with a couple of other great European nights against [teams such as] Liverpool, the atmosphere was incredible.
"That's what it felt like last night."