They went onto win 43-31 in one of the biggest shocks in the tournament's history. His death follows that of the other number 11 on the field at Twickenham in 1999 - Jonah Lomu who passed away five years ago.
Dominici would come off the bench eight years later when France upset the All Blacks at the biggest stage in rugby once again - the 20-18 win at Millennium Stadium. He retired from test rugby at the end of the 2007 tournament.
"It is with immense sadness that the Stade Francis learns of the death of Christophe Dominici," his former club said in a statement.
"A rugby genius and companion without equal, he will leave a great void in our big family. Our thoughts go to his family, his wife Loretta, and his daughters Chiara and Mia."
"He left his mark on a whole generation of rugby," the French Rugby Federation said. "Today the rugby family has brutally lost a legend, an emblematic player."
At club level, he won five French championships in a glittering 11-year spell with Stade Francais, having started his career with hometown club Toulon.
Tributes were widespread for Dominici, who was well-liked by fans, teammates, and opposing players alike.
"Thanks Domi for all you gave to French rugby and all the good times I spent with you," former France winger and teammate Vincent Clerc said on Twitter.
World Rugby called him "an all-time great of the game" while the English and Irish federations were quick to offer their condolences.
Jonny Wilkinson, who played club for Toulon late in his career, chose to pay his tribute on Twitter in French.
"The death of Christophe Dominici is terribly said," he wrote. "We are thinking of all of his loved ones. The whole of sport has lost a true legend."
- With AP