The very careful way in which Tolkien used varieties of language in LOTR: Roughly modern English for the "Common Speech", angloAnglo-saxon and somewhat antique English for Rohan, quite formal for Gondor, Norse names (but not actual Norse) for people Dale and for Dwarves, etc,etc; is perhaps hard for most authors to achieve, and many readers miss its subtleties. (But do read the section of Shippey's The Road to Middle-Earth on the Council of Elrond, where this is discussed in some detail.)
I would advise against an American/Spanish or English/French distinction, or other obvious use of a "real" accent, such as is described in the answer by hszmv, unless this is an SF work set in the future where cultures clearly descended from current ones are present. I for one find such out-of-place cultural artifacts distracting. But some consistent distinction is speech could be a good thing. Another
Another thing one can do, as mentioned in the answer by KeizerHarm, is describe speech in terms of the reactions and associations notesnoted by characters who hear it. For example:
These show some of the ways in which character perception of speech patterns can tie into other aspects of character. They are a little clichedclichéd, but then I just dashed them off, and have invented what context they have. (They are not from any work in progress or real work.) But they should serve as examples of the sort of thing I am talking about. Note that I have mixed informal descriptions of manners of speaking, such as "sharp", "quick", "low", and "growly" with more subjective evaluations such as "fancy" and "crass", non-standard spellings such as "what'n" and "talks", and emotional reactions such as Bolar's resentment, Marik'Marik's disdain, and Falma 'sFalma's alarm. In my view such a mixture works better than any one of these alone. But even so, this is easy to over do-do -- passages like these examples should be scattered, and fairly rare, or the reader will revolt and abandon the book.