In case you and your partner are not yet married, our first piece of advice is that you and your partner get legally bound.
Indeed married couples face a lot of requirements, let alone individuals who do not have any legal bond.
As a student a visa applicant is not authorized to work and earn any income. Therefore, his/her dependent (spouse or child) must provide evidence of his/her own financial resources during the entire stay in France when applying for a visa. The dependent will get a visitor's visa and will not be authorized to work either.
Of course, if the partner/spouse is employed in France, it is an entire different scenario.
In case you are not married nor legally bound, your partner will be considered as a long stay visitor and will have to provide the French consulate with solid financial resources.
Also please bear in mind that ESSEC can only validate the enrollment status of students. Private visa or residence permit applications must be handled by individuals.