Per the Wikipedia page about her [1], the two Nobel prizes that would have made sense for her to be awarded were both granted after her death — one in 1962 and another in 1982. The Nobel isn’t awarded posthumously.
And the NP is never shared by more than three individuals, so the one in 1962 probably wouldn't have been awarded to her even had she been alive. But the one in 1982 probably would have been hers to share if she had lived.
[1] https://en.m.wikipedia.org/wiki/Rosalind_Franklin