What insight of Watson and Crick was missed by Franklin?

Franklin did realize that the structure was the double helix independently, but she did not have time to construct a detailed model based on the diffraction data by the time Watson and Crick constructed theirs. Prior to the publication there was a meeting, and the content of Nature papers, and the splitting of the credit, were agreed upon in advance by both groups. Here is the timeline from Cobb's Life's Greatest Secret:

"Franklin’s laboratory notebooks reveal that she initially found it difficult to interpret the outcome of the complex mathematics... but by 24 February, she had realised that DNA had a double helix structure and that the way the component nucleotides or bases on each strand were connected meant that the two strands were complementary, enabling the molecule to replicate.

[...] To prove her point, she would have to convert this insight into a precise, mathematically and chemically rigorous model. Watson and Crick had already crossed the finishing line – the Cambridge duo had rapidly interpreted the double helix structure in terms of precise spatial relationships and chemical bonds, through the construction of a physical model.

In the middle of March 1953, Wilkins and Franklin were invited to Cambridge to see the model, and they immediately agreed it must be right. It was agreed that the model would be published solely as the work of Watson and Crick, while the supporting data would be published by Wilkins and Franklin."

Curiously, Watson's sexism might have prevented him from having any competition altogether (although, naturally, he was more concerned about Pauling than Franklin, whom he called 'Rosy' in print):

"Ironically, the data provided by Franklin to the MRC were virtually identical to those she presented at a small seminar in King’s in autumn 1951, when Jim Watson was in the audience. Had Watson bothered to take notes during her talk, instead of idly musing about her dress sense and her looks, he would have provided Crick with the vital numerical evidence 15 months before the breakthrough finally came."