Another two-nouns-stapled-together translation. The real phrase already exists.

What a Japanese person actually thinks
Reads like the title of a civics textbook chapter. Completely inert.

Literally: freedom + spirit
Actually: Parseable as 'a spirit of freedom' — but as a description of a person it doesn't work. It sounds like the name of a policy platform.

Naturalness●●●●●

Nobody says this. The established yojijukugo for 'free spirit' is right there and it's better in every way.

Coolness●●●●●

None. It's four characters of nothing.

Nothing embarrassing lurking in here.

自由奔放 jiyū honpō
free and unrestrained; doing as one pleases

The actual established phrase. Same four-character density, and it genuinely describes a person.
風来坊 fūraibō
a wanderer; someone who drifts where the wind takes them

If you mean free as in untied rather than free as in unrestricted. Warm, slightly romantic, very human.

自由精神

Orientation: either

N/A — change the words.