Hi,
"have" is the "prescriptively correct" one, because it actually and grammatically refers to "languages".
Now, the fact is that a lot of native speakers use the singular in those kinds of structures, because they make the verb agree with what comes before "one of".
The advice is: use the plural when you feel you will be judged on strict grammar rules (= ESL Tests), otherwise use either one, depending on what you have in mind, what you are thinking of.
Venusian is one of the
languages that
don't have the subjunctive. --> You are thinking of the languages that don't have the subjunctive, and Venusian is one of them.
Venusian is one of the languages that
doesn't have the subjunctive. --> You are thinking that Venusian doesn't have the subjunctive, along with other languages.

Oops, that's true for American English... I don't know if you are interested in BrE.