Jacquelin saw off the challenge of Chile's Felipe Aguilar and Germany's Maximilian Kieffer during a prolonged play-off battle after the trio finished the final round tied on five under par following a collapse by Scot Marc Warren.
The Frenchman went head to head with Kieffer on the 18th after Aguilar was knocked out following the third play-off hole.
The duo battled it out in the joint-longest European Tour play-off since its formation in 1972, with a decider in the 1989 Dutch Open the only other sudden death to run to a ninth hole.
The play-off, which lasted two hours, ended when Jacquelin hit a wedge to five feet from the hole and finishing off for a three-shot birdie.
"That is very tiring by I am really, really happy," Jacquelin told europeantour.com after the epic finale.
"I could not make any putts (in the play-off) but the last one dropped, which means a lot for me and my family."
He added: "There's another baby coming at the end of November; every time I get a baby, there's a win so I'll have a football team after a few years!"
The win is Jacquelin's first on The European Tour in just over two years.
The play-off was set up after overnight leader Warren bogeyed three of his last six holes to slip out of contention.
It was reminiscent of last year's Scottish Open, where Warren was three clear late on and went on to throw away the lead
However, it looked as if he would hold on to claim victory as despite dropping a shot on the second he claimed a birdie on the par five third hole and carded par on the fifth.
But then it all started to go wrong, as a dropped shot on the next when an eight-foot putt refused to sink and back-to-back bogeys at the 14th and 15th meant Aguilar, who was in the clubhouse after a round of 70, joined him at the top of the leaderboard.
A birdie on the 16th gave the Scot a brief glimmer of hope, but two more bogeys on the final two holes left him four over par for the round and out of the play-off showdown.