The 30-year-old form Orthez was the only player in the final three groups to shoot under par as she carded a final round 5-under-par 67 to reach 7 under par.
Arricau, who becomes only the third French player to win their National title, finished two shots ahead of Austrias Natascha Fink who had best of career second place finish with a final round 72.
Tied for third place on 3 under par were Australian Jane Leary and Swedens Linda Wessberg, who kept in touch with the Frenchwoman until her 16th hole when she made a double bogey.
But it was Arricau who raced out of the blocks with four birdies in her first six holes to jump into contention. While the remainder of the leaders were watching each other and failing to make any headway, Arricau, who won her first title in La Corua three weeks ago, took the outright lead on the par-5 13th hole where she two putted from 30 feet.
Despite a bogey after at the dogleg 15th hole after a pushed, the diminutive Frenchwoman redressed the balance with a birdie at the 16th from 6 feet.
Managing to avoid dropping a shot at the notorious 17th hole, which saw 30 players have bogey or worse, Arricau approached the last hole with great caution, knowing that she almost threw the tournament away in Spain after she had a double bogey and slipped into a playoff.
Having safely negotiated the final hole three groups ahead of the leaders, Arricau was not taking any chances and had a nervous wait for Fink, who had to eagle the final hole. With the green out of reach in two shots and Fink not managing to pull off the miracle shot, Arricau screamed with relief.
I did the same score last year in the final round, so I was thinking about that all day long, said Arricau, who joins Patricia Meunier-Lebouc and Marie-Laure de Lorenzi as the only French players to win the Womens French Open.
I think this win was more difficult than La Corua because when I began the day playing very well, I knew very quickly that I was in contention.
Its an incredible feeling now and when I got on to the flight to Spain, I could not imagine that I would be having three weeks like this. When I won there, I knew I could win again and the start I made today, that really helped a lot.
Anja Monke from Germany closed in a tie for fifth spot alongside South African Laurette Maritz, Englands Lora Fairclough and third round leader Ǻsa Gottmo, who closed with a disappointing final round 76.
And defending champion Lynnette Brooky closed in a four way tie on one under par with Gwladys Nocera and Natalie David from France and Gina Scott from New Zealand.