I've always heard it pronounced as archbishop indicates - how do you think it is pronounced, then we can get a consensus from our colleagues on the AB?
English-speakers pronounce it as 'Reems', as has been said here, but I believe the French pronounce it as 'Wrongs' but with the final 's' as in 'snake', rather than the 'z' sound it usually has at the end of words. (What I'm suggesting is roughly what you yourself suggest, Thewillow.)
Ok- I was taught frog by a parisian so the accent is a bit variable, but it is pronounced RAMS...but the m is so under pronounced in ths context that it can sound like rance. the a is pronounced as in ram, though (or slam). The r is rolled and the s is hissed. so really it could be written HRRAmSSS
bernardo's answer is closest to the demonstration I just received from my French colleague (Merci, Antoine) who prounced it "rANhss". Imagine Inspecteur Closeau saying 'rince', or a slightly less-comic French accent saying 'trance' without the T.
Yes, Mango, her father was Caius Farquahar whose mother was Uxellodunum Cholmondley, a French land owning family at Thugny-Trugney. Their daughter, Valentinianu Cholmondley married Themistogenes Mainwaring of Dizy-le-Gros and Nizy-le-Comte. Their daughter, Atlantiades, married Dromachetus Rheims and lives at Sommepy-Tahure. Oiradgh's sister, Mariandynum, married Peucedonus Cholmondley and lives at Chuffilly-Roche. They all pronounce Reims as "rames".