Can I apply for a k1 visa if I currently have a student visa?

I see no reason why you would not be able to apply for a K-1 petition for your fiancée in France while you are a student in France. You would of course have to submit the I-129F petition to the appropriate USCIS service center in the US and use your US address as your place of residence. The petition would take approximately 9 months until your fiancée interviews with the American Embassy in Paris. Upon approval, you can both go back to the States. You will of course have to marry within 90 days of your fiancée's entry, and she will have to apply for adjustment of status to permanent residence thereafter. Due to the limitations of the lawyers.com forums, Alan Lee, Esq.’s (the firm) participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting the question. No attorney/client relationship is or shall be construed to be created hereby. The information provided herein by the firm is general and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice, nor as the basis for making any decisions of legal consequence.

Your US citizen fiancé will need to apply for you.  Your student status won't affect the application.