Repose, orginally a verb meaning ‘to lie at rest’ taken into english from middle french reposer, which itself was evolved from old french repauser, all meaning the same thing. repauser comes from the late latin repausare (“to cause to rest”), constructed from the latin re- prefix, used as an intensifier, slapped onto the latin verb pausare (“to stop”) [this is the stem of the word ‘pause’, btw]. the noun form of repose meaning “state of rest” is a back formation from the verb form.

There’s also a second verb form of repose: “to put/to place”. That one is constructed from the latin repos-, which is the stem of the latin verb “reponere”, which meant “put back/set back/replace/restore”, constructed from latin re- (not as an intensifier this time, but in it’s stem form of “back/away”) + ponere “to place”[which is also where the word ‘position’ comes from, as the past participle of ponere is positus]

The second verb form has no connection to either the noun or first verb form. {Besides the connotations in english with regards to the usage of “to place” being a synonym of “to rest on”. The two forms have similar meanings but non-connected etymological background, which is why I originally said this.}