Formal:
* Rédiger un mémoire: This is the most formal way to say it, and it implies a long, academic paper.
* Rédiger un rapport: This also implies a formal paper, but it can be shorter than a mémoire.
* Rédiger un document: This is a more general term for writing any kind of document, including a paper.
Informal:
* Écrire un devoir: This is a more casual way to say "to write a paper", often used in the context of school assignments.
* Écrire un texte: This is a very general term for writing anything, including a paper.
Example sentences:
* Je dois rédiger un mémoire sur l'histoire de la France. (I have to write a paper on the history of France.)
* Le professeur nous a demandé de rédiger un rapport sur nos recherches. (The professor asked us to write a report on our research.)
* J'ai écrit un texte sur la pollution atmosphérique. (I wrote a paper about air pollution.)
The best way to say it depends on the specific situation. If you're unsure, it's always best to err on the side of formality.