What should I do with a paper I've translated? Aside from reaping the personal benefits, what should one do after translating a paper? It would be nice to offer it to others, but I assume it is a copyright violation to post it online. Sending it to the author(s) to deal with seems like a safe but potentially presumptuous option.

(Motivation: I recently tried my hand at translating a paper from French into English,  Quasi-positivité d'une courbe analytique dans une boule pseudoconvexe by Michel Boileau and Stepan Orevkov.)
If the paper you are speaking about is a published research paper, you should contact the publisher (e.g., Springer), as they do deal with copyright issues. If the paper is a technical paper, written by a set of authors about a subject, and those papers are hosted on an university website or a research-based company, then you need to contact the authors. 

If the paper is not a research or technical paper, then well the question is not related to the Academia section.