Why does everyone speak french in Montenegro?

Well it seems that way at the Casino they do, and they seem to have French accents. The croupier seems to speak French at the Poker table in certain words here and there. The book is set in Franch, but the movie is moved to Montenegro, so shouldn't the characters working in the hotel have accents to that country?

French is/was the official language of European casinos - even in Morocco (Casablanca) and England (Dr. No). And remember, in Fleming's day, the croupier only called  to "Messieurs" as it was assumed that ladies didn't gamble.

Oh okay, but Montenegro is much more Eastern Europe though, and was a former slavic socialist area of the former Yugoslavia. Would a place like that still have French as the official language in a casino there?

Because the producers couldn't be bothered to do it properly by setting it in a Royale-les-Eaux.

Yes they would still speak French in a casino because it's how it works.