Spanish is an adjective.
It's possible to say 'Spanish one', but not usually for a person. You would probably say, for example:
'The Spanish athlete won the race'
'The Spanish runner won the race'.
Spaniard is always a noun. (sustantivo)
So you could say 'The Spaniard won the race'.
Note that you can say 'the Spanish' but this has a different meaning. If you say 'the Spanish' you are referring to the Spanish nation as a whole. For example, 'The Spanish tend to eat dinner fairly late in the evening'.