Grothendieck called "schemes" schémas in French. I find it strange we call them schemes. In fact, Grothendieck called them (pre-) schemas(this is an English word) in his talk(in English) at Proceeding of the international congress of mathematicians at Edinburgh in 1958. There is an English word schema which means almost the same as French schéma. I think English words schema and scheme have different meanings and nuances although they are similar. So who first called Grothendieck's schéma scheme in English? And why he did not call it schema?
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Let’s see whether I can get my memory working right on this. It tells me that I was in the seminar that G gave at Harvard in 1958-59(*), I was a second-year grad student then. He talked about schemes, of course, and he did so in English. He certainly must not have called them “schémas” (pronounced shayma in French), because none of us called them that in discussions. So I hope I’m right in saying that G himself called them “schemes” from the get-go. And he would have made this decision, I’m fairly confident, on the advice of Tate.
(*)Maybe it could have been 1959-60; but those are the only two possibilities.
Interesting etymology question. Although this is not a proper answer, maybe "scheme" was preferred to avoid overlapping with schema/schemata of axioms in logic? In fact, as Zhen Lin remarks in his comment, the use of scheme/schema in logic is done without distinction so the same should be possible in algebraic geometry. In French, Italian and Spanish I have always seen "schéma/schema/esquema", in books, classes, lectures... which are closest to its Greek origin σχῆμα / skhễma (« manière d'être », « forme », « figure », « extérieur », « apparence », « faux-semblant »). For example in the classic Grothendieck's EGA and SGA, or Perrin's modern French book (and many other references), they use "schéma/schémas". In German they also say "schema, schemata". But in French there is also "schème", so maybe in the original works and translations, one was more favored than the other. The differences are subtle just as their English equivalents:
Since in most of the other languages, at least in Europe, "schéma/schema-schémas/schemata" are the most used, I think there should be no problem to do the same in English as synonymous without changing meaning.
Nevertheless "schème" has a particular specific meaning in Philosophy since old times: Immanuel Kant's defined schèmes as processes or means by which a pure concept becomes effective by the implication of an intuition. In French, it has been used since then in philosophy and psychology in the form "schème" instead of "schéma", and is still used so nowadays.
Finally, from a purely linguistic and etymological point of view, the most natural correspondence between English-French would be "schème $\rightarrow$ scheme" and "schéma $\rightarrow$ schema". As I commented in the other answer by Lubin, maybe the phonetics of pronouncing [skiːm] seemed more natural to English speakers than ['skiːmə]. Despite being pronouced "sh" in French, in German, Spanish and Italian the sound is the same as in English [sk] and we nevertheless stuck to the [-a] ending.
My personal opinion, given all the above remarks, would be that "schema/-s-ta" are the best suited form even in English for being Grothendieck's original choice in French (despite having "schème" at his disposal! and despite the sociological evolution in conferences as Lubin recalls in his answer), and because it would then coincide with the uses in other languages and avoid other meanings of "scheme" (see the funny commentary of Asaf below). I personally always use "schéma/-s" in the same way as people use "étale topology/cohomology" and "étalé space" instead of the possible translations "calmed topology/cohomology" and "spread-out space" (which would sound to me as weird as other perverse names, like "perverse sheaf"). But maybe there are deeper reasons, for example, in Romance languages we use "valeur propre/valore proprio/valor propio" where the English speaking world took mainly the Germanic analogues "eigenwert/egenwerd", but I have seen both uses in English also "proper values = eigenvalues".