Let me modify your question a little. Here is a full(er) quote extending yours:
'“Because he has despised the word of the Lord”; this is a reference
to one who says the Torah did not originate from Heaven. And even if
one says the entire Torah originated from Heaven except for this
verse, i.e., any one verse, claiming that the Holy One, Blessed be He,
did not say it but Moses himself said it on his own, this is included
in the category of: “Because he has despised the word of the Lord.”
And even if one says the entire Torah originated from Heaven except
for this inference [דקדוק] inferred by the Sages, or except for this kal v'chomer [ק"ו], or except for this gezeirah shavah [גזירה שוה], this is
included in the category of: “Because he has despised the word of the
Lord.”' [Sanhedrin 99a]
Notice that the same verse, "he has despised the word of the Lord" applies both to the written Torah (one verse, etc.) and to the oral Torah. It is all "the word of the Lord".
Now within the oral Torah there is an easy answer to your question. See Menachos 30a, concerning the last eight verses of the Torah:
אלא עד כאן הקב"ה אומר ומשה כותב ואומר מכאן ואילך הקב"ה אומר ומשה כותב בדמע
Until this point, i.e., the verse describing the death of Moses, the
Holy One, Blessed be He, dictated and Moses wrote the text and
repeated after Him. From this point forward, with regard to Moses’
death, the Holy One, Blessed be He, dictated and Moses wrote with
tears
Here the gemara is discussing the last eight verses and the ones just before - all part of the "narrative" portion of the Chumash, and it says that they were dictated by G-d and transcribed by Moshe.
In that same section,
אמר לו ר"ש אפשר ס"ת חסר אות אחת וכתיב (דברים לא, כו) לקוח את ספר התורה
הזה ושמתם אותו וגו'
Rabbi Shimon said to him: Is it possible that
the Torah scroll was missing a single letter? But it is written that
God instructed Moses: “Take this Torah scroll and put it by the side
of the Ark of the Covenant” (Deuteronomy 31:26), indicating that the
Torah was complete as is and that nothing further would be added to
it.
(I wonder if the gemara refers implicitly to the verse before that one as well, as it uses the phrase עד תומם - "When Moshe finished writing the words of this Torah in a book, until they were completed.")
You see that at this point, what was until then completely oral (I'm leaving out a side machlokes about when various parts were written), and all from Hashem, was partially converted into the written part of the Torah. That unity known as a "Sefer Torah" was complete at that point and given over to Israel for safekeeping.
So in the oral tradition, your question is easy. If you are asking, though, Are there internal proofs within the Written Torah (as one sees, for instance about Megillas Esther, see gemara Megillah 7a), I'm not giving an answer. But the written and oral Torah are interlinked to such an extent [see also Shabbos 31a] that I do not think that such a demand would make sense - though it's an interesting request.
[By the way, I think that there is actually no dichotomy between "narrative" and "halachic" parts of the Torah. Even the halachic parts are really narrative: they each are enveloped in phrases like, G-d spoke to Moshe saying... Imagine if the Shulchan Aruch began with a phrase, R' Yosef Caro spoke to his students, saying...! The Chumash is really all one big story, so to speak.]
