Jackson is currently struggling to take a full part in training but he is expected to do so on Thursday, with the Irish camp hopeful he will be fully fit to take his place in the No10 shirt at the Aviva Stadium two days later.
"Paddy's chances of pulling through are very good and he should be good to train on Thursday," said Ireland head coach Declan Kidney.
"We'll make the choice between Paddy and Ian (Madigan) then. I was told 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."
Jackson's Ulster clubmate Craig Gilroy has been ruled out with a groin injury so Fergus McFadden starts on the wing, while Cian Healy and Mike McCarthy are named in the pack after returning from suspension and injury respectively.
Tom Court and Donncha O'Callaghan are the men to make way for loose-head prop Healy and second row McCarthy, with the former looking like missing out on a place in the matchday squad altogether.
Head coach Declan Kidney has left the tight-head prop and fly-half spots on the bench vacant, with Ian Madigan set to back up Jackson if the youngster is passed fit and Michael Bent and Stephen Archer in line to cover Mike Ross after Declan Fitzpatrick succumbed to a calf problem.
Ireland (versus France, Aviva Stadium, Saturday 5pm)
Rob Kearney (Leinster); Fergus McFadden (Leinster), Brian O'Driscoll (Leinster), Luke Marshall (Ulster), Keith Earls (Munster), AN Other, Conor Murray (Munster); Cian Healy (Leinster), Rory Best (Ulster), Mike Ross (Leinster), Mike McCarthy (Connacht), Donnacha Ryan (Munster), Peter O'Mahony (Munster), Sean O'Brien (Leinster), Jamie Heaslip (Leinster)
Replacements: Sean Cronin (Leinster), David Kilcoyne (Munster), AN Other, Donncha O'Callaghan (Munster), Iain Henderson (Ulster), Eoin Reddan (Leinster), AN Other, Luke Fitzgerald (Leinster)