The French is okay, because I'd guess that in English we'd say this as "France Press Agency". For the initials, I suppose the pronunciation of the letters in English ("ayee-eff-pee") is as good as "ah-eff-pay".
If you want to translate the words in the name into English, you must also change the word order to be correct in English: French Press Agency.
However, here, France-Press is the name of a specific agency. I wouldn't translate it any more than I would render "Charles de Gaulle" in English as "Charles of the long pole used to beat fruit from trees*." My preference would be to refer to the France-Presse Agency.
*Nobody knows exactly how this name originated. Other possible derivations have also been suggested. Feel free to substitute your favorite.
The Google Books Ngram Viewer indicates that writers in books do not translate the name -- neither entirely nor just the word "Agence".
If you can read entangledbank's phonetics above, I would suggest you go with that
(with stress on the second syllable of "Agence"? And perhaps [ɛ] -- open mid-front vowel -- in "Presse").
If the nasal vowel [ã] is difficult, I think it would be acceptable in English to render it as [an].
"France" would rhyme with "Agence" here, and both would rhyme with "wants"
(unlike my usual pronunciation of the name of the country, [frænts]), rhyming with "pants"..
Likewise for [ɹ]: If the French uvular "r" is a problem, your English "r" would be acceptable (I guess that's the meaning of the inverted "r" in phonetics).
Erm, okay, Loob. It's just that some people, maybe many, wouldn't know what AFP by itself stands for. But if you said "Agence France Presse", in whatever accent, people would, indeed, figure it out (just as, for example, French people would understand what "Associated Press" or "United Press International" means).