Sunderland's Andy Reid and Coventry's Clinton Morrison are also out of the party named by Trapattoni on Friday for the two-legged play-off against Les Bleus at Croke Park on November 14 and Stade de France on November 18.
Trapattoni recently said he did not think Steven Reid would play again following injury, a statement which drew a furious response from the player's club manager Sam Allardyce.
The Rovers chief had labelled the Italian's suggestion the 28-year-old may never recover sufficiently from his injury problems to continue his career at the highest level "disgusting" and "disgraceful" - and called for an unequivocal apology.
Asked about Trapattoni's opinion that it would "be very, very difficult" for Reid to regain his peak form and fitness after a year of injury woe, the Rovers manager had said: "There's no player more honest than Steven - and to be dealt that sort of a blow at this stage, when he's not feeling the best, trying to come back from a big injury and picking up another little niggle, is very, very disrespectful to say the least.
"I'm not happy with what Trapattoni said. I'm disgusted with it.
"It's disgraceful, completely out of order. He's undermined us as a football club and Steven as a player."
But announcing his squad on Friday, Trapattoni remained unrepentant even though Reid scored a penalty and played for 70 minutes of Blackburn's 5-2 Carling Cup fourth-round tie win over Peterborough.
It was the same for Finnan who has only recently returned to action with Portsmouth following injury and Andy Reid who has starred in midfield for Sunderland this season.
Trapattoni said: "This team now is balanced. I cannot change now.
"It is not the time to change the team now. We have a mentality (to beat France), we cannot change the team now."
The Italian added: "We performed strongly throughout the qualifying group stages.
"We were undefeated in all 10 games and this is a reflection of how we have played and also the mental strength of this team."
Despite the strength of the opposition, Trapattoni believes his Republic squad showed enough during the group stage of the qualifying campaign, where they finished second behind Italy in European Group Eight.
Trapattoni added: "France have a strong squad but we go into this play-off knowing that we are only 180 minutes away from qualifying for the World Cup."