You have to know, that, in the official French doctrine (in metropolitan France), there are no races, and skin colours should be officially ignored. I´d avoid referring to races and skin colours in Metropolitan France when it´s not related to the topic of the current conversation.
Asians (Chinese, Vietnames, Thai, Japanese etc looking people) can be referred as "de type asiatique" (something I would avoid if I´m dressing these people). You can also say "de type Vietnamien/Coréen/Chinois" if you can tell for sure.
North-Africans are often referred to as "Arabes" or "Maghrebins" (I avoid using "Maghrebin" when talking to an Arab because it is implying he or she is an Algerian, a Tunisian, or a Morroccan citizen). The police uses the expression "de type Nord-Africain".
Using "verlan" crypto-slang (obtained by mixing the syllabs of a word) is often considered correct in informal speech, for example among youngsters : Arab = arabe -> Beur/Rebeu , Black = Noir -> renoi. I wouldn´t use it, but it isn´t considered offensive on the street or among friends or young people. Some people use the word "Black" to avoid saying "noir".
We don´t really use any word for Hispanic people, as they are basically whites (sometimes one can say "de type sud-américain").
Sometimes you can hear old people talking about Nègres and Négresses in a non-offensive way (until WWII it was the main word). Some african intellectuals in the 1970s aroung Senghor used it extensively in the context of the "Négritude" movement.
As far as I know, in the French Antillas, it´s not offensive to talk about someone being a Métis, Mulâtre, Quateron, Béké (White Creoles, stereotyped as rich and inbred), etc. But it is a very specific social context.