Should I invoice or should I get a CDD?

I am in profession liberale working as a life coach, and recently was hired to teach 4 hours a week at a private school of higher education. I will have a contract for 15 weeks, but it has not been finalized. I have the choice of billing the institution for “honoraires” or having a contrat de travail à durée déterminée (CDD). I’m beginning to think the CDD may be wiser, although it may complicate my accounting and/or income tax declaration. For example, wouldn’t a CDD would give me more rights as worker? Isn’t there a limited amount of times the CDD can be renewed before they are obliged to make it a contrat à durée indéterminée (CDI)? If so, both of these are potentially important.

My main goals for taking this job:

1. Increased stable and regular income
2. Being associated with a prestigious organisation
3. Increasing my activity in my original field, which is not regulated, and for which I have a diploma and 15 years previous experience

Also, I am a registered formatrice professionelle with the Direction Régionale du Travail, de l’Emploi et de la Formation Professionnelle (DRTEFP), so the courses I create and teach in personal and professional development are exempt from TVA. Am I right in thinking that if I did invoice the school for my honoraires as a formatrice, that the DRTEFP-granted TVA exemption still applies? It would require adding the field of study to the list of topics taught on the annual DRTEFP bilan declaration. Bottom line, should I invoice or should I get a CDD?