It’s not a double negative. Both negative words are active. 

“She can’t not touch” means she is unable not to touch it, but is compelled to touch. 

“She cannot refrain from touching it” perhaps seems more comfortable, but “refrain” also has negative force. 

See John Lawler’s answer to https://english.stackexchange.com/questions/113541/origin-and-correctness-of-ain-t-no/113582#113582 for more on negatives and negative polarity.