The Italian translation of 'free spirit' is spirito libero. Another expression that you may hear in Italian and which has much the same meaning is anima libera, which refers to a 'free soul'.
The word libero means free, and comes from the same Latin root as the English words liberty or liberation.
'Free of cost' in Italian
To refer to something being 'free', as in 'not costing any money', Italians would use the word gratis, which derives from the term gratuito, or 'without payment'.
You may find this word emblazoned on the shelves of Italian supermarkets as part of the phrase compri due ricevi uno gratis which translates to 'buy two and recieve one free'.
Free spirits in popular Italian culture
As you can imagine, the concept of a free spirit is one that rings true to many artists, musicians, writers and other creative types. This is perhaps the reason behind many Italian pop songs having the idea of a free spirit as their theme, an example of which is the 2003 release by the Italian songstress Giorgia entitled spirito libero. As its topic, the song lyrics examine society's role in encouraging our need for freedom whilst imprisoning us in a cage of expectations.