Even the English are confused. There are very subtle differences in English between to assume, which one should avoid doing as it makes an 'ass' out of 'u' and 'me', (i.e. it may later be your downfall if you didn't check your facts) to presume which perhaps suggests some knowledge which you are perhaps checking and to suppose which might be more of an ambivalent or undecided agreement with something but most of this is lost on most English speakers and context is probably more important than which word you choose.... Someone English or American is bound to disagree...
very Latin againn : presuponer in Spanish , presupporre in Italian,présupposer in French , pressupor in Portuguese. all from LATIN praesumere with the idea of to suspect ( the Latin praesumere has many more significations, like" to presume " for instance.
Those come instead from Medieval Latin praesupponere, present active infinitive of praesuppōnō. From prae (“before”) + sub- (“under”) + pōnō (“put, place”). From praesūmere, praesūmō come "presumir" (Sp.), "presumire" (It.), "présumer" (Fr.), "presume" (En.). In Spanish, "presumir" usually means "to boast", but it can also mean "to assume", especially in some fixed idioms, like "presunción de inocencia", "presumption of innocence".