The in-form winger admitted afterwards that it had been a bittersweet day for him, "That sums it up pretty much," he said. "I'm obviously delighted to get on the scoresheet.
"It's very difficult to be able to score a try or two tries at the Stade de France but to come away with nothing out of it, or a draw, is very disappointing."
Bowe, who turned 28 last month, has now scored 24 Test tries for Ireland. He demonstrated exactly why he has been so successful with the opening score early in the first half, as he cleverly intercepted Aurelien Rougerie's pass and darted in behind the posts.
"We knew that they like to throw the ball out to Rougerie in that area and Darce (Gordon D'Arcy) and Keith (Earls) went up and closed him down," he explained.
"So, just doing my job, I have to kind of close that off in case he does throw that pass and luckily I was able to get in between it."
The Monaghan native almost got in for another intercept try before a brilliant individual effort in the 38th minute left Ireland 17-6 in front at the break.
"We were obviously extremely upbeat at half-time. We were very positive before the match and I think that we really took it to them in the first half. I think second half we knew we had to continue the same thing.
"And second half it was very difficult, a real turnaround in the game. Whenever we got into their areas of the pitch we seemed to make a few small errors that we didn't make in the first half."
The draw ends a long losing run for Ireland in Paris but, having led for so long, Bowe said the outcome felt more like another defeat.
"Yeah, it did without a doubt. A draw is obviously, I suppose, meant to be a good result over here," added the Ospreys clubman.
"Probably our second best result we've had in over 20 or 40 years, but I think that we gave ourselves every opportunity today to come away with a win. And to not score a point in the second half is very disappointing."