Falloir only has one conjugation: “il faut”, meaning “it is necessary” then followed by another verb in the subjonctif.
Has falloir always been incomplete in this way, or in the past was it a normal verb with a regular conjugation pattern that gradually evolved into an incomplete verb?
More forms in Old French Edit: it looks like the defective falloir is just a variant of the perfectly normal faillir.
https://fr.m.wiktionary.org/wiki/falloir
It’s been that way since at least the 1100s, but I don’t think the Latin word it gradually evolved from (fallere) was used that way in Roman times, so the usage developed sometime in the Middle Ages.
(Actually, according to that link, it was passive until the 1400s, when the current construction developed.)
So from “faillir” meaning “to almost do something”, there was a singular off-shoot meaning “necessary to do something”. Those do seem close meanings. Interesting.
It can also be an infinitive.
Not to dispute that there’s only 3rd person singular forms, but there’s also ‘il fallait’ and ‘il faudrait’.
Rather “to miss”, or, quite obviously, “to fail”(English stayed more faithful to the original meaning), via expressions like “so little was missing to achieve whatever”, to the idea that the little thing is what is required, hence that the verb means “to need”, “to require”.