Captain Thierry Henry appeared to handle the ball twice before feeding Gallas, who bundled home from close range on 103 minutes to give France a 1-1 draw in the return leg at the Stade de France.
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Henry first stopped the ball from going out with his arm, then controlled it with his hand in the penalty area and then crossed for the defender to give France the edge after they had struggled for most the game.
"I just received the ball at the far post and went for it," Gallas told French television when asked whether he had noticed any infringement by Henry in the build-up to a goal certain to stir a heated debate.
The Ireland players protested but Swedish referee Martin Hansson did not hesitate to award the goal, enabling the World Cup runners-up to book a trip to next year's finals in South Africa after a shaky qualifying campaign.
Ireland captain Robbie Keane had put the visitors ahead and levelled the tie at 1-1 on aggregate shortly after the half-hour, tapping home from inside the box a fine backward pass from the left by winger Damien Duff.
France, who won the first leg 1-0 at Croke Park on Saturday, looked nervous and clumsy until the closing stages while Ireland kept pushing and had the better chances.
"It was tough, laborious at times, miraculous at others but I only knew one thing, that it would be a 1-1 draw and we would qualify," France coach Raymond Domenech, whose job was on the line, told French television.
BROKEN NOSE
The home side, who lost central defender Julien Escude, injured in a clash of heads with team mate Patrice Evra early on and later diagnosed with a broken nose, looked vulnerable at the back throughout the match.
The former world and European champions also showed little initiative up front but will nevertheless appear in their fourth successive finals while Ireland failed to make their fourth overall after 1990, 1994 and 2002.
Ireland tried their luck and would have enjoyed a better fate without a string of brilliant saves from France keeper Hugo Lloris, who had the 79,000 crowd packing the arena where France lifted the World Cup in 1998 chanting his name.
The first two clear chances were for Ireland shortly before the half-hour, first when Lloris dived in front of a lurking Keane. Seconds later, Kevin Doyle headed the ball wide from close range.
France survived another scare on 73 minutes, Keane rushing into the area and past Lloris but then pushing the ball too far.
It was not until extra time that France woke up, threatening with an angled shot by Nicolas Anelka that went wide. Substitute forward Govou then hit the back of the net but was ruled offside.
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