His replacement Paddy Jackson struggled with his goal kicking on Sunday and Ireland coach Declan Kidney came in for criticism for his selection of the Ulster youngster.
Paddy Jackson with Ulster coach Mark Anscombe
Lock Donnacha Ryan is also a doubt after sustaining a shoulder injury at Murrayfield while his fellow second row Mike McCarthy continues to nurse the knee problem which ruled him out of the Scotland defeat.
"Donnacha suffered a bruised AC joint. He won't take part in training this week and will be reassessed on Monday. At this stage he is in some doubt for France," Kearney said.
"Mike is running well and is improving, but he has a number of milestones to reach before being available for selection. At this stage we'd rate his chances of being fit at 50-50."
Wing Craig Gilroy sustained a groin strain at Murrayfield but should be able to resume training early next week.
However, Gordon D'Arcy's foot injury will be remain in a protective boot for another week so he looks certain to miss the France game.
Ireland's successive Six Nations defeats have led to intense speculation that Kidney's Ireland contract will not be extended beyond this summer but the coach has continued to deflect questions about his future.
"I haven't been thinking about that," he insisted.
"My only concern is to help this team do as well as they can do. That's my reason for being here.
"We have a match against France next weekend and that's all I'm concentrating on.
"There are huge highs and lows that go with this job and last Sunday was a big low, especially after having created so much."
Kidney has also come under fire for handing the captaincy to Jamie Heaslip, who replaced the vastly experienced Brian O'Driscoll as skipper before the Championship, but the coach reiterated his faith in the Leinster number eight.
"Jamie's done an excellent job for us. He's making good decisions and I'm very happy with him," Kidney said.
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