While I believe there may have not been a term of "Free Spirit" in Latin, if we were to translate it and retain its English meaning using Latin words, what would it be?
I would translate that as animus liber. I think liber (free, unrestrained, not subordinate to anything) and animus (soul, mind, will, consciousness, intellect, rationality) match what "free spirit" means. To get a better feeling of these two Latin words, I suggest taking a look at any online Latin dictionary.
Calling a person an animus in Latin seems analogous to calling a person a "spirit" in English. It is the same kind of metonymy, and works well in my opinion. This is not an attested classical idiom as far as I know, but should be easily understandable to the Romans in a suitable context.
The English “free spirit” is a bahuvrihi compound meaning “whose spirit is free; having a free spirit”, of the same structure as Latin magnanimus “whose spirit is great”. The German equivalent of “free spirit” is “Freigeist” – patently a compound – which Grimm & Grimm & alii, “Deutsches Wörterbuch”, gloss as “liberioris judicii in rebus divinis”. I think “liberi judicii” works quite well for “free spirit”.
Animus is perfectly appropriate in this context but I think that, rather than liber, either effrenatus or effusus would better express the idea of a spirit that is 'free' here.
The two adjectives are very close in meaning. Effrenatus, 'unbridled' means 'lacking (external) control', while effusus indicates that the spirit enjoys an extraordinary freedom of expression.