Maybe this question is too obvious, but… if you wan to use a library available for Matlab/Octave in a “completely free open-source code without the need of reimplementations”, why don’t just use Octave?
Octave is completely free open-source, and you woudn’t need to reimplement anything. I’m pretty sure that using the library directly in Octave will work far better than trying to use Julia or any other engine with Octave code, except maybe Matlab.
EDIT: After re-reading, I understand your point better: You want to use the Octave functions as part of your study, but the rest you want to do it in Julia, right?
If that’s the case, I don’t know of a straightforward solution. There have been some attempts in the past, e.g. MatlabCompat.jl, but I don’t know of any one which has not been abandoned. If you say what’s the library you want to use, maybe someone can tell if there is a convenient alternative for Julia.