Cowen raised the issue of replaying the match with his French counterpart at a European Union summit in Brussels on Thursday after French captain Thierry Henry admitted he handled the ball in the build-up to William Gallas's winning goal in Paris.
Sarkozy said he was sympathetic to Ireland's position, but could not support Cowen's call for restaging the game.
"I told Brian Cowen how sorry I was for them," Sarkozy told reporters.
"But don't ask me to substitute myself for the referee, or the French football authorities, or the European football authorities: leave me right where I am."
Cowen earlier backed an appeal by the Football Association of Ireland to football's world governing body FIFA to have the game replayed.
"Yes, I do (support the FAI). Our minister of sport will write to FIFA in support of that complaint and look for a re-match," he said.
"He (Sarkozy) would understand the sense of disappointment that the Irish people feel after the tremendous performance last night I think that fair play is a fundamental part of the game."
The FAI have asked FIFA to order a replay of the controversial World Cup play-off against France.
Irish football authorities said the extra time goal at the Stade de France, which gave France a 2-1 aggregate win and dominated news bulletins in Ireland all day, as well as being discussed in parliament, had "damaged the integrity of the sport."
Citing a decision to invalidate the result of a World Cup qualifier between Uzbekistan and Bahrain in 2005 as a precedent, FAI chief executive John Delaney said he was not calling for a replay simply out of principle.
FIFA officials told Reuters that any replay would need the agreement of both football associations before the governing body could consider such an appeal.
