But 28-year-old Bowe was in no mood to stick to the script, looking to rip it up completely as his two first-half tries gave Ireland a 17-6 half-time lead.
However France hit back in an enthralling second half scoring 11 unanswered points, including a try from Wesley Fofana, to set up a grandstand finish that almost led to a French win but for some resilient Irish defence.
And while a draw in Paris is far from a disgrace, Bowe admitted he would swap personal glory for team victory any day.
"We put them under pressure in the first half but failed to score in the second half which was disappointing," said the winger, who has scored five tries in this season's Six Nations.
"To score two tries in Paris is a great achievement but nobody enjoys coming away with a draw. We showed good composure to in the last ten minutes.
"Our first half display was outstanding but we were under a lot of pressure at the end and did well to avoid giving away a penalty, which was crucial."
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