I have read in many places that Parah could be a biblical requirement to read.
Why is that? Zachor makes sense (as it says so in the Torah here). Why Parah?
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The Beit Yosef in OC 685 quotes Tosfot who says that Parashiyot Zachor and Parah are Biblical requirements. However, our versions of Tosfot do not have anywhere that Parah is Biblical. The Mishna Berura OC 685 sk 15 writes that most Achronim agree that Parah is not a Biblical requirement. So we really don't know what source Tosfot had in mind (assuming the Beit Yosef's version didn't have a scribal error, which is possible).
וְהָיְתָה לִבְנֵי יִשְׂרָאֵל וְלַגֵּר הַגָּר בְּתוֹכָם לְחֻקַּת עוֹלָם
...and it shall be unto the children of Israel, and unto the stranger that sojourneth among them, for a statute for ever.
The sifra derives from here that the ashes remain effective even nowadays without the Temple. However, later on the pasuk repeats (Numbers 19:21):
וְהָיְתָה לָהֶם לְחֻקַּת עוֹלָם
And it shall be a perpetual statute unto them.
The Aruch HaShulchan posits that this extra occurrence of the phrase comes to teach that one should be involved even without the ashes by learning these verses which we do by reading them publicly once a year.
Again, this is all speculation because we don't have an original derivation (as I explained above).
I think that Tosfos in Berachos 13a is the source for where the idea of Parshas Parah being d'oraisa stemmed from.
If you look at the Tosfos below, you'll see that Tosfos lists the Torah portions that are d'oraisa, and only Parshas Zachor is mentioned:
However, earlier printed versions of Maseches Berachos have this same Tosfos who mentions Parshas Zachor AND Parshas Para:
I remember learning that this is the source for where the confusion stemmed from- ie whether Tosfos actually meant it, or whether it may have been a printer's error etc.
Many years ago I heard that the basis for Parshas Parah being biblical is from this verse: זְכֹר אַל־תִּשְׁכַּח אֵת אֲשֶׁר־הִקְצַפְתָּ אֶת־יְהוָֹה אֱלֹהֶיךָ בַּמִּדְבָּר. Remember, don't forget how you angered your Lord in the desert. The Torah then goes on to talk about the sin of the golden calf. Now Rashi tells us that the Parah Adumah, the red heifer was to atone for the sin of the golden calf. So when we read about the red heifer before Pesach, we remember the sin of the golden calf and we remember how we angered the Lord in the desert. It was so long ago (over 50) that I don't have a source for this idea.