Andy Farrell's side was undone by an early red card for Peter O'Mahony against Wales, but it was Ireland's failure to capitalise in the 10 minutes when France was down to 14 that proved key this time around.
Charles Ollivon scored the first of two France tries while it was undermanned, giving the visitor an advantage they never surrendered.
France led 15-3 five minutes before the hour and, although a spirited revival gave Ireland hope, the host could not complete a turnaround, meaning its championship prospects are effectively over. France, by contrast, goes into the first rest weekend top of the table.
Matthieu Jalibert and Billy Burns each missed early penalties before Burns knocked a simple one over to give Ireland a 3-0 lead.
The host was then boosted further when Bernard Le Roux was shown a yellow card for tripping during a kick-chase.
James Lowe looked to have taken an immediate advantage when he went over in the left corner but the TMO ruled he had been pushed into touch by the scrambling France defence.
Ireland was punished for not taking that chance in stunning fashion as a wonderful France attack, in which the ball was intricately worked to the right and then back left, ended with Gael Fickou sending Ollivon over.
Jallibert added the extras and landed a penalty shortly before the interval.
France wasted a golden opportunity to go further ahead after a superb carry from Julien Marchand before Ireland's task was made more difficult when Cian Healy and Iain Henderson clashed heads in a tackle.
Ed Byrne and Ultan Dillane entered the fray as replacements for their bloodied team-mates but could not help Ireland wrest control of the game away from France.
The visitor's command was strengthened in the 57th minute when Jallibert looped a long pass out to Brice Dulin, who shrugged off a defender and fed Damian Penaud for France's second try.
Yet Jallibert failed with the conversion and, after Ollivon was penalised from the kick-off, Ronan Kelleher marked his introduction by strolling over following a fortunate bounce at a line-out.
A long-range penalty from Ross Byrne trimmed the gap to two points and Jallibert failed to respond in kind nine minutes from time as he struck the upright from 51 metres.
But as in Cardiff last week, Ireland failed to produce a dramatic final say and will likely be playing for little more than pride for the rest of the tournament.