While the usual adjective is "Spanish" - Spanish food, Spanish language, Spanish culture etc. in the case of time zones, it appears to be the convention to use the name of the country or city. The GMT website uses 'Spain time'. Likewise, 'Australia time', not 'Australian time'. Interesting question - I have never thought about it before!

It might sound more natural to say 'Time at Spain'.

Spanish time. You use an adjective to modify a noun.

I would say Spanish time but Spain time would probably be fine as well.