Sexton missed the 12-8 defeat by Scotland with a hamstring injury and team manager Mick Kearney has revealed that his chances of returning for the must-win encounter are receding.
"Jonny continues to make progress. He's back running this week but to reach match level intensity there's still significant work to do," Kearney said. "At this stage we are more hopeful than confident of his availability for France. We would say it's somewhat less than 50-50."
Lock Donnacha Ryan is also a doubt after incurring a shoulder problem at Murrayfield, while his second row partner Mike McCarthy continues to nurse a knee problem. The prognosis over Craig Gilroy's groin complaint is better, however, with the Ulster wing expected to train next week.
"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. Craig Gilroy suffered a groin strain but scans excluded a tear. He continues to improve and should train fully next week."
Ireland's Six Nations has imploded amid an awful injury-list and successive defeats to England and Scotland, with the loss of a match in Edinburgh that they dominated particularly damaging.
The results have seen calls for Declan Kidney to step down escalate, but the head coach is focusing only on inflicting a fourth successive championship defeat on France.
"I haven't been thinking about that. My only concern is to help this team do as well as they can do. That's my reason for being here," Kidney said. "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."
The erratic leadership of Jamie Heaslip, who replaced Brian O'Driscoll as captain before the championship, has been identified as a weakness, but Kidney has backed the Leinster number eight. "I'm aware there are frustrations out there. 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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