France, the 1998 champions and 2006 runners-up, drew 1-1 with Ireland at the Stade de France in the second leg of their play-off for a 2-1 aggregate win yesterday.
But the extra-time triumph came in controversial circumstances when French skipper Henry appeared to control the ball with his hand before his angled pass allowed William Gallas to head in the crucial 103rd-minute goal.
Ireland, who had deservedly levelled the tie through Robbie Keane's 32nd-minute goal, protested desperately, but in vain, to match referee Martin Hansson.
"On the goal, it all happened so quickly," said Gallas.
"I received the ball from Thierry (Henry). It happened so quickly that I couldn't see (if the ball hit his hand)."
In Zenica, a 56th-minute strike by Raul Meireles was enough to break Bosnian hearts and send 2006 semi-finalists Portugal through to the finals.
The Portuguese, once again without the injured Cristiano Ronaldo, had won a hard-fought first leg 1-0 courtesy of a close-range header by Bruno Alves on Saturday and again had to be on their mettle.
Meireles took a pass from Manchester United star Nani and slipped a low, precise shot past Kenan Hasagic in the Bosnian goal to settle the tie.
"These marathons are only over after the final whistle and I want to thank my players for showing such spirit," said a Portugal coach Carlos Queiroz.
Bosnia, trying to reach the World Cup for the first time, had midfielder Sejad Salihovic red-carded late in the game, a decision which caused the match to come briefly to a halt with one of the linesmen appearing to have been struck by an object thrown from the crowd.
Guus Hiddink, who famously took South Korea to the 2002 semi-finals, will be missing from South Africa after Slovenia beat his Russian side 1-0 in Maribor to qualify on the away goals rule.
Striker Zlatko Dedic, who plays his club football for Bochum in Germany, scored the only goal just before the break.
Russia had won the first leg 2-1 in Moscow on Saturday, but Nejc Pecnik's goal two minutes from time gave Slovenia hope for Wednesday's return leg and they seized their chance to reach their first finals since 2002.
Hiddink's side ended the match with nine men after Alexander Kerzhakov and Yuri Zhirkov were both red-carded.
In Donetsk, Greece beat Ukraine 1-0 to book a World Cup finals place for the first time since 1994.
Panathinaikos striker Dimitris Salpingidis netted the only goal of the match for the 2004 European champions following Saturday's 0-0 draw in the first leg in Athens.
"I'm proud of my players. They put all of their heart and soul into today's match," said Greece manager Otto Rehhagel.
"It was really tough to contain Ukraine's attacks throughout the match but we did our best and luckily we managed to do it and achieve the desired result."
In total, 13 European nations will play in the 32-team World Cup finals with the draw set for Cape Town on December 4.
Netherlands, England, Spain, Germany, Denmark, Serbia, champions Italy, Switzerland, Slovakia, Greece, Slovenia, Portugal and France/Ireland make up Europe's representation.
