Could she win the French Open?
I say yes.
Or, what if she just developed a much more reliable first serve?
Errani made it to the final last year, and she did it--stunningly--by taking out two former French Open champions, a former French Open finalist and Angelique Kerber. Against Maria Sharapova, she was unable to win a set. Sharapova, in addition to having a better serve (unless she's double-faulting like mad) and a lot of power in her groundstrokes, has also learned a lot more about how to move on clay.
At any rate, Errani is capable of doing some damage in Paris this year, too. She certainly doesn't have the mental issues some top players have, and she fights to the end.