I can come to the rescue with the university-provided resource of the OED! (Although this could arguably be a better question for a true historical linguist.)

Porno- Etymology:

Shortened < pornography n. and pornographer n. Compare ancient Greek πορνο- , combining form (in e.g. πορνοβοσκός brothel-keeper) of πόρνη prostitute < an ablaut variant of the base of περνάναι to export for sale ( < the same Indo-European base as πέρα beyond: see far adv.) + -νη , suffix forming nouns, as prostitutes were often bought slaves. Formations occur from the first half of the 20th cent.

Pornography as an English term may have been in part borrowed from the French pornographie, meaning treatise on prostitution (1800), obscene painting (1842), description of obscene matters, obscene publication (1907 or earlier). The earliest OED citation for the use of 'pornography' in published English-language works is 1842: W. Smith Dict. Greek & Rom. Antiq. 694/1: "Rhyparography, pornography, and all the lower classes of art [....]"

Meanwhile, fornicate comes from the LATIN (as opposed to greek) and a distinctly metaphorical meaning. Etymology:

Latin fornicāt-, participial stem of fornicārī of same meaning, < fornic- , fornix brothel, originally arch, vault

From my own years studying latin, I know that they were fond of using any noun that indicated concavity as a euphemism for vagina (sinus, meaning bay or water inlet; vagina itself, meaning sheath for a sword, etc.) So I think that the "vault" meaning probably became slang for vagina, and then referring to prostitutes as mere vaginas, rather than 'arch' referring to the physical building of a brothel, which is how the Greek term developed.

So, separate language roots, deceptively similar sounds!

EDIT Also, fornicate was introduced into the english language much earlier! OED earliest use citation goes back to 1552: R. Huloet Abcedarium Anglico Latinum: "Fornicaten, or commit fornication or lechery, fornicor." If I had more time on my hands, I would run both words through google n-gram for their respective uses in english over time, which could be fun.