Arricau eventually signed for a 1-under-par 71 to reach nine under par total alongside Scott, who had a 3-under 69 to sneak into the playoff.
Becky Brewerton from Wales took third spot alone on 8-under-par after a 71 for her second top three of the season but could not take full advantage of her laser-like iron play on the back nine as her putter went cold at the wrong time.
With nobody making a significant move forward after the first nine holes, Arricau stretched away and seemingly had the title in the bag after a blistering back nine when she notched up five birdies in six holes to lead on 11 under par heading to the final hole ahead of Scott, who kept the pressure on with two birdies and an eagle of her own on the homeward nine.
Then the drama began. Leading by two from the Kiwi coming uphill at the 18th, the Frenchwomans approach to the green hit one of the tall conifers and rebounded back into a similar position.
From there, the former French and Spanish amateur champion punched the ball under the branches of the offending tree, leaving two putts from 30-feet for the win, should Scott miss her 20-foot birdie chance.
Scott did miss and Brewerton, who had birdied three of the last six holes to reach eight under, let her final chance slip by from 8 feet.
Arricau had no more than three feet uphill for the win, but the ball slipped by on the left for a double bogey and echoes of Jean Van de Veldes classic 1999 Open Championship farce were whispered in the gallery.
But where Arricaus male compatriots Van de Velde and also Thomas Levet in the 2002 Open Championship, failed to take the opportunity in playoffs, Arricau did. At the first extra hole, it would be Scotts turn to miss a short putt as the Frenchwoman safely negotiated the tricky closing hole in par for her maiden victory.
I was feeling really good after those birdies and I remembered that Jean-Luis Guepy had seven birdies in a row and I was trying to equal that, said Arricau, who was soaked by bottled water by her fellow French Ladies European Tourists after the win.
I was comfortable all the way in, but at the final hole, I just played the second shot too quickly and it was not a good shot. But I thought that I could just get it on, make bogey and I would still win.
But now Ive done it, Im really happy, but I couldnt believe the other players soaked me with water ' it should have been champagne!
Scott, who won her only title on the LET at the 2000 Chart Hills Classic after beating Isabella Maconi from Italy in a playoff, was magnanimous in defeat.
Its all I could do to get into the playoff, said Scott.
I played the back nine well and thats all I could ask for but Stephanie played great all day long.
Brewerton, who was looking to become the first rookie on the LET to win since 2001, hit 15 greens in regulation and was disappointed, despite finishing with her fourth top three on the LET, twice as an amateur and twice in this, her rookie season.
I did all the damage on the front nine, said Brewerton, who made double bogey on the eighth hole when she was tied for the lead.
I had so many good chances out there and lipped out a couple of times and I wasnt quite there on all of the others.