Gulbis shot a 2-under 70 in the final 18 holes of regulation to finish the French event at 4-under 284. It was her first tour title.
Jang, who didn't get a taste of the lead until her birdie on the 18th sent her into the playoff, managed an even-par 72.
It was a disappointing day for Juli Inkster, who led after three rounds only to stumble to a 3-over 75 Sunday. She wound up tied for third at minus-three with Ji-Yai Shin (72) and women's world No. 1 Lorena Ochoa (68), who shared the low round of the day with Suzann Pettersen.
Michelle Wie shot a 76 that left her at plus-16.