From what I understand, someone on a long stay student visa (France) may get a part time work permit if s/he is studying at a university or institue of higher education that is affiliated with French social security. Are there are any schools in Paris which teach French as a foreign language (to adults, not in a degree program) and are also affiliated with French social security?
You can ask to the local town halls in Paris, they organise often adult courses or have information on them. Also you might contact organisation of language courses.