Fill a large dutch oven with a few inches of oil, and attach a candy thermometer to the side. Heat the oil over medium heat to 375°F. Working in small batches, use tongs to add the green beans to the batter and toss to coat. Remove from the batter, shaking off any excess and lower the green beans carefully into the preheated oil. Fry, turning once, until golden. Remove and transfer to a paper towel-lined baking sheet. Sprinkle with fleur de sel while still warm. Repeat with the remaining batches of beans and serve immediately.