Captain Paddy Jackson got the Irish off the mark before the break and as Mike Ruddock's side turned the screw, Horan used his strength and speed to worm his way over for an opportunist 43rd minute try.
Jackson converted from in front of the posts but France, with their powerful scrum providing a welcome platform, bounced back with two more successful kicks from Otazo.
Nevertheless, Ireland showed a huge amount of grit when surviving a sin-binning for flanker Aaron Conneely and keeping France at day in a superb display of dogged defending.
French number 8 Karl Chateau thought he had burrowed his way over for a last minute try, but television match official Derek Bevan could not confirm the grounding and the visitors hung on for Ireland's first ever away win over France at Under-20 or Under-21 level.
"It was a bit of a dogfight but we got a very important try from Foster. It was an excellent individual effort (from him) and we tackled and competed for the 50-50 possession very well," Ruddock told the Irish Examiner.
"In the end it was a sort of a scary moment when the referee and TMO came into it. France thought they scored a try at the death but it was shown not to be a try on the replay.
"There's always drama when an incident like that happens in the 79th minute and you wonder whether the decision is going to go your way or their way, but it was inconclusive."
The Ireland U-20s' efforts in defence have been hugely encouraging in their opening two Championship games, with Wales failing to score a try in Athlone and the French also held tryless.
It is an aspect of their game that has undoubtedly pleased Ruddock to date, but with matches against Italy, Scotland and England still to come he knows he has plenty to work on with the players in both defence and attack.
"I thought it was fantastic defending by our lads (at the end) because we got lots of bodies around the ball carrier, got our hands under the ball and stopped what might have been a clear-cut try being scored.
"We have created some very good chances in both games to date, but haven't always nailed those and you need to do that in matches that are as close as they have been.
"There has been a lot of spirit and a lot of courage, though, and to win in France is no mean feat, so we'll take that in going forward," he added.
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