Jackson, who endured a mixed afternoon when deputising for the injured Jonathan Sexton against Scotland, has suffered a hamstring strain that has placed his participation in slight doubt.
The uncertainty over the 21-year-old's fitness and the presence of the in-form Madigan has prompted coach Declan Kidney to delay naming his selection for the number 10 jersey and who will supply cover from the bench.
Sexton was set to be recalled but it was decided this afternoon to give him a further week in his rehabilitation from the hamstring injury sustained against England.
"Paddy's chances of pulling through are very good and he should be good to train on Thursday," Kidney said.
"We'll make the choice between Paddy and Ian then. I was told just a moment ago that it will be better to give Jonathan Sexton another week to recover.
"Jonny ran at top speed this morning. It would be easy to put him in against France, but it's better that he builds up his strength for another week."
In total there are three confirmed changes to the starting XV defeated by Scotland, among them Fergus McFadden's selection on the right wing after Craig Gilroy failed to recover from his groin strain.
Cian Healy is restored at loosehead prop after completing his suspension for stamping against England on February 10, replacing Tom Court.
Lock Mike McCarthy has recovered from the knee ligament damage sustained in the loss to Stuart Lancaster's Grand Slam-chasing team, so Donncha O'Callaghan drops down to the bench.
Donnacha Ryan continues in the second row after passing a fitness test on his bruised shoulder.
Substitute prop Declan Fitzpatrick has also been ruled out with a calf strain and his replacement has yet to be announced.
Ireland record's against pre-tournament favourites France is dismal having registered a solitary victory in their last 13 meetings - the Grand Slam-winning year of 2009 - in a sequence dating back to 2003.
But the form of the winless French has been even more startling and they are seeking to avoid a first championship whitewash since 1957 and first wooden spoon since 1999.