(@Monica Cellio asked that I expand my comment into an answer.)
The beginning looks like a top voice to me because of its 3-fold repetition in semibreves D-D-D then breve C. The lowest line of the page looks to me like a tenor that could go with it: D D Eb F F F -- it doesn't exactly work, but it gives me a sense of what might be implied here.
If it is meant to be in Locrian, I would want to see a number of Ebs -- mode in the Renaissance isn't just final notes and key signatures, but also the usage and distribution of notes. There are only two notes a fifth above the cadential A and they're both neighbor tone minims. The D and A are much more prominent notes, letting me think that it's a mode with D and A as the final and co-final/reciting-tone.
There's an argument from a Bayesian/probabilistic standpoint -- the Locrian mode is not a mode that is discussed in any medieval or Renaissance treatise (I actually stumbled on this question while deciding whether to post a question about the earliest reference to the term "Locrian" -- I suspect it's 19th c.). Thus, to me there's an assumption that it won't be in Locrian unless it's very clearly there. I can't imagine that a piece designed to teach dance moves would also be the most harmonically innovative piece in a century without the author having commented on it. It seems more likely that the rhythms + contours are the most important elements for this discussion (esp. given the lack of clefs)
So none of this is to say that it's absolutely impossible to say that it's in the Locrian mode -- it could be an incredibly innovative genius choosing to hide his or her invention of a new harmonic system in an obscure place. People have made these arguments for a number of pieces, but I always find that another explanation (incorrect clefing in some works; painters who didn't care about painting music with accuracy in the case of music in art works) is more compelling.