"Paddy kicked in the Aviva Stadium yesterday and kicked well and trained fully this morning," said Ireland team manager Mick Kearney.
"He came through kicking at the Aviva Stadium yesterday afternoon very well, so that clarified things for us, but up until then there was some small doubt.
"There was no discomfort this morning so he'll be fine."
Jackson made his Test debut in the absence of the still injured Jonathan Sexton just under a fortnight ago as Ireland lost 12-8 to Scotland at Murrayfield.
He received mixed reviews on his international bow after a disappointing goalkicking display and his failure to fire Ireland to victory despite a mountain of possession.
But Kidney was quick to praise the 21-year-old's performance in Edinburgh and had no hesitation in keeping the Ulsterman in the hot seat if he could prove his fitness.
Jackson's ability to do just that means there is no place in the matchday 23 for triple Lions tourist Ronan O'Gara, who had been left out of the initial squad but tipped for a recall if the youngster failed to pull through.
Uncapped Ian Madigan of Leinster has been named as reserve fly-half, meaning there is no place for Ireland' most capped player, sparking fresh doubts about the future of the 36-year-old's international career.
The third sport left vacant by Kidney has also been filled, with Munster prop Stephen Archer picked on the bench ahead of Leinster's New Zealand import Michael Bent.
Saturday night's fixture in Dublin will potentially be the 25-year-old's first cap having previously represented his country at A level with the Wolfhounds.
Ireland (versus France, Aviva Stadium, Saturday 5pm)
Rob Kearney (Leinster); Fergus McFadden (Leinster), Brian O'Driscoll (Leinster), Luke Marshall (Ulster), Keith Earls (Munster), Paddy Jackson (Ulster), 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), Stephen Archer (Munster), Donncha O'Callaghan (Munster), Iain Henderson (Ulster), Eoin Reddan (Leinster), Ian Madigan (Leinster), Luke Fitzgerald (Leinster)