A sociology of language would seek to understand the way that social dynamics affect individual and group language use. It would have to do with who is 'authorized' to use what language, with whom and under what conditions. It would have to do with how an individual or group identity is established by the language that they have available for them to use. It would seek to understand individual expression, one's (libidinal) investment in the linguistic tools that one has access to in order to bring oneself to other people.
The key figure in th establishment field is Joshua Fishman, founder and still editor of the International Journal of the Sociology of Language.