It does sound like Renaissance, but it may be early Baroque as well. It sounds like a lot like this work:
http://www.youtube.com/watch?v=4EVBZWKcPag
This is credited as a sinfonia in Claudio Monterverdi's "Il ritorno d'Ulisse in patria" although a poster said the piece is actually the "sonata seconda" by Giovanni Battista Grillo. This was added music to I guess make the missing pieces more complete for Monteverdi's whole work.
If this isn't actually it, I hope it helps you find the actual piece and composer.