"Not only X, but also Y" is rarely used to modify a subject of a sentence as in your example as there are more concise ways to convey the same message as JCG mentioned in the comment.
(1) Neither Sarah nor Jim liked Paris.
(2) Both Sarah and Jim disliked (hated)
(3) Sarah and Jim both disliked (hated) Paris.
Comparing your example with the (1) sentence, you can see it is far more concise than your example while there is no change in its meaning.
If you really have to use "not only X, but also Y", it is better to change "not like" to "dislike (hate)" as it clears the confusion that the two "not's" might cause. Of course, the functions of the first "not" and the second "not" are different, but it is better to use an alternative if there is one available.
"Not only Sarah, but also Jim disliked (hated) Paris".
You can visit Cambridge Dictionary Grammar Site to see more examples of how the construction works. There is not a single example that shows "non only X, but also Y" modifies a subject.
Not only did she forget my birthday, but she also didn’t even
apologise for forgetting it.
If you rephrase it to:
Not only did she not remember my birthday, but she also didn’t
even apologise for not remembering it.
It is less confusing than your example as "not only X, but also Y" modifies verbs and the sentence is inversed.