We did fill out ds-160 before having all the paperwork ready. I don't think it really matters. Did your embassy send you a form (paper or online) to fill out once you are ready for the interview ?
Basically the way it works for France is that we have to fill the DS-160 (whenever we want and print your confirmation page), gather all the papers asked and once you are done you send back to the embassy a form of readiness so they know they can schedule your interview.
Anyway ! We filled ours before receiving packet 3 and no problem at all Just need your embassy case number to fill it out.
Hope that helps ! You can also read the page of your embassy on the website : http://www.visajourney.com/consulates/index.php?ctry=Romania&cty=Bucharest
Looks like your equivalence for our readiness form in France will be your confirmation page of the DS-160 and the passport informations.
Good luck ! You are almost done with the K1 process that is really exciting