Green had seven birdies to lead by two strokes in the European Tour event, but Storm picked up a shot on the 17th to bridge the gap with Green after the Australian bogeyed the same hole.
"It's nice to see my name on the leaderboard, especially coming out on 18," said Storm, who won the French Open in 2007. "You kind of remember that you've won it before and you've been in this position before."
Italian teenager Matteo Manassero shot a 68 to share sixth place with 10 others, after recovering from a double bogey on the second hole by making an eagle on the next.
Four players were disqualified for a rules violation after hitting into the water on the last hole.
Rikard Karlberg of Sweden, Damien McGrane of Ireland, James Ruebotham of England and Jaco Van Zyl of South Africa all dropped their balls from the wrong place. Only if the ball went beyond a certain point were players allowed to use the drop zone.
"The local rules are very clear," European Tour senior referee Andy McFee said. "It says at the 18th hole, the drop zone can only be used if the last point of entry is beyond the green stake.
"Players have to read and understand the local rules. Players spend hours and hours on the practice round trying to save a shot. Well, five minutes in the rule book can have exactly the same effect."